More conjectures!

[Ralf Stephan]

You are asking for work, do you know, Antti?

> > Good work your list of hundred,
> >when we will get the next one? .-)

Unfortunately, math is no longer my main interest today.
But exactly this and your question is the reason to 'open my archive'
with conjectures with this eMail!

Ta-daa.

The following lists for each of my OEIS conjectures the entry line
and the name line of the sequence (to get an idea about it). The
list was gathered using the Makefile at the end which can be easily
adapted to your liking.

Have fun!
 
%C A000057 Numbers so far are a subset of A064414. - Ralf Stephan, Aug 19 2004
%N A000057 Primes dividing all Fibonacci sequences.
%C A000063 Appears to contain every Catalan number (A000108). - Ralf Stephan, Aug 19 2004
%N A000063 Symmetrical dissections of an n-gon.
%N A000130 One-half the number of permutations of length n with exactly 1 rising or falling successions.
%C A000130 Partial sums seem to be in A000239. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 28 2003
%F A000184 Appears to be 2 * A029887(n). - R. Stephan, Aug 17 2004
%N A000184 Number of rooted planar maps with n edges.
%C A000239 First differences seem to be in A000130. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 28 2003
%N A000239 Number of permutations of length n by rises.
%F A000804 Conjecture: G.f.: x^5 * (-65*x^10 - 94*x^9 + 88*x^8 + 170*x^7 + 323*x^6 + 267*x^5 - 242*x^4 - 232*x^3 - 216*x^2 - 95*x + 120)/(x^11 + x^10 - 2*x^9 - 2*x^8 - 4*x^7 - 2*x^6 + 6*x^5 + 2*x^4 + 2*x^3 - 3*x + 1) - R. Stephan, Aug 05 2004
%N A000804 Permanent of a certain cyclic n X n (0,1) matrix.
%Y A000879 Is the same as A083270? Ralf Stephan, Feb 17, 2004
%N A000879 Number of primes < square of n-th prime.
%N A001188 Number of even graphs with n edges.
%C A001188 a(n) appears to be [A060639(n) + 1] / 2. - Ralf Stephan, Aug 21 2004
%F A001277 Apparently the partial sums of A000166. - R. Stephan, May 23 2004
%N A001277 Number of permutations of length n by rises.
%C A001335 Appears to be 6*A003289(n-1), n>1. - R. Stephan, Mar 25 2004
%N A001335 Number of n-step polygons on hexagonal lattice.
%C A001337 Appears to be 12*A003287(n-1), n>1. - R. Stephan, Mar 25 2004
%N A001337 Number of n-step polygons on f.c.c. lattice.
%C A001896 Appears to be the same as A033474 - Ralf Stephan, Feb 17, 2004
%N A001896 Numerators of cosecant numbers; also of Bernoulli(2n,1/2) and Bernoulli(2n,1/4).
%N A001986 Let p = n-th odd prime. Then a(n) = least prime congruent to 3 modulo 8 such that Legendre(-a(n), q) = -1 for all odd primes q <= p.
%C A001986 Numbers so far are all 19 mod 24. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 07 2003
%C A001988 Numbers so far are all 7 mod 24. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 07 2003
%N A001988 Sequence of prescribed quadratic character.
%C A001990 Numbers so far are all 5 mod 24. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 07 2003
%N A001990 Sequence of prescribed quadratic character.
%C A002273 Numbers so far are also terms of A002520. - R. Stephan, Aug 23 2004
%N A002273 Theta series of 28-dimensional Quebbemann lattice.
%N A002430 Numerators in Taylor series for tan(x). Also from Taylor series for tanh(x).
%C A002430 a(n) appears to be a multiple of A046990(n) (checked up to n=250). - R. Stephan, Mar 30 2004
%C A002462 Appears to divide A002894(n+1). - R. Stephan, Aug 23 2004
%N A002462 Coefficients of Legendre polynomials.
%C A002463 Apparently, a(n) divides A000894(n). - R. Stephan, Aug 05 2004
%N A002463 Coefficients of Legendre polynomials.
%N A002553 Coefficients for numerical differentiation.
%C A002553 Numbers so far divide A052469(2n+1). - R. Stephan, Aug 24 2004
%F A002571 Appears to have g.f. x/[(1-3x+x^2)(1+x)^2]. - R. Stephan, Apr 14 2004
%N A002571 From a definite integral.
%C A002659 Conjecture: a(n) = 2*sigma(n) - 1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 26 2004
%N A002659 Related to planar partitions.
%F A003258 Conjecture: a(n) = A078489(n) + n - 1. - Ralf Stephan, Feb 24 2004
%N A003258 Related to Fibonacci representations.
%F A003440 G.f.: {(1-x)^2 * sqrt[(1+x+x^2)/(1-3x+x^2)] + x^2 - 1}/(2x^2) (conjectured). - R. Stephan, Mar 28 2004
%N A003440 Number of binary vectors with restricted repetitions.
%N A003441 Number of dissections of a polygon.
%F A003441 Numbers so far suggest that two trisections of sequence agree with those of A050181. - R. Stephan, Mar 28 2004
%F A003668 The first differences seem to have period 26. - R. Stephan, Mar 28 2004
%N A003668 a(n) is smallest number which is uniquely a(j)+a(k), j<k.
%F A003787 Numbers so far appear to equal A053290(n)/2. - R. Stephan, Mar 30 2004
%N A003787 Order of universal Chevalley group A_n (3).
%F A003788 Numbers so far appear to equal A053291(n)/3. - R. Stephan, Mar 30 2004
%N A003788 Order of universal Chevalley group A_n (4).
%F A003789 Numbers so far appear to equal A053292(n)/4. - R. Stephan, Mar 30 2004
%N A003789 Order of universal Chevalley group A_n (5).
%F A003790 Numbers so far appear to equal A053293(n)/6. - R. Stephan, Mar 30 2004
%N A003790 Order of universal Chevalley group A_n (7).
%F A003791 Numbers so far appear to equal A052496(n)/7. - R. Stephan, Mar 30 2004
%N A003791 Order of universal Chevalley group A_n (8).
%F A003792 Numbers so far appear to equal A052497(n)/8. - R. Stephan, Mar 30 2004
%N A003792 Order of universal Chevalley group A_n (9).
%C A003841 Is a(n) = A007531( A00961(n)+1 )^2 ? - R. Stephan, Feb 08 2004.
%C A003841 Numbers given so far divided by 36 (except the first) are all members of A014796. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 07 2004
%N A003841 Order of universal Chevalley group D_2 (q), q = prime power.
%N A004130 Numerators in expansion of (1-x)^{-1/4}.
%F A004130 a(n) = prod(k=1,n, (4k-3)/k * 2^A007814(k)), proved by Mitch Harris, following a conjecture by R. Stephan.
%F A004134 Conjecture: a(n) = 3n - A000120(n). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 13 2003
%N A004134 Denominators in expansion of (1-x)^{-1/4} are 2^a(n).
%F A004134 a(2n) = a(n) + 3n, a(2n+1) = a(n) + 3n + 2 (conjectured). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 07 2003
%N A004443 Nimsum n + 2.
%F A004443 The sequences 'Nimsum n + m' seem to have the general o.g.f. p(x)/q(x) with p,q polynomials and q(x) = (1-x)^2*prod[k=0..inf, 1+x^(2^e(k))], with sum[k=0..inf, 2^e(k)] = m. - R. Stephan, Apr 24 2004
%N A004735 Denominator of average distance traveled by n-dimensional fly.
%F A004735 a(2n) = A001803(n) (conjectured). - R. Stephan, Mar 10 2004
%F A004762 G.f.: x/(1-x) + x^2/(1-x)*[1/(1-x) + sum(k>=0, 2^k*x^(3*2^k-1))] (conjectured). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 05 2004
%N A004762 Numbers n such that binary expansion does not begin 100.
%F A004793 (3-n)/2 + 2*floor(n/2) + sum(k=1,n-1,3^A007814(k))/2 (conjectured). - Ralf Stephan, Feb 24 2004
%C A004793 Also conjectured: a(n) = b(n-1), with b(0)=1, b(2n)=3b(n)-2-3[n odd], b(2n+1)=3b(n)-3[n odd] (checked 384 terms). - Ralf Stephan, Mar 01 2004
%F A004793 Seems to equal A003278(n) + [n is even]. - Ralf Stephan, Apr 06 2004
%N A004793 a(1)=1, a(2)=3; a(n) is least k such that no three terms of a(1), a(2), ..., a(n-1), k form an arithmetic progression.
%F A005590 Conjecture: a(3n)=0 iff n in A003714. - Ralf Stephan, May 2 2003
%N A005590 a(0) = 0, a(1) = 1, a(2n) = a(n), a(2n+1) = a(n+1)-a(n).
%C A005683 Appears to be a bisection of A068930. - R. Stephan, Apr 20 2004
%N A005683 Numbers of Twopins positions.
%C A005686 Appears to be the pairwise sums of A001687. - R. Stephan, Apr 21 2004
%N A005686 Number of Twopins positions.
%N A005924 From solution to a difference equation.
%F A005924 Numbers so far satisfy a(n) = A000557(n) - 1. - R. Stephan, May 23 2004
%N A006428 Tree-rooted planar maps.
%F A006428 a(n) seems to be divisible by n+1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 01 2003
%N A006432 Tree-rooted planar maps.
%F A006432 a(n) seems to be divisible by n+1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 01 2003
%F A006468 G.f.: (5+2x-4x^2+x^3)/(x-1)^7 (conjectured). - Ralf Stephan, Apr 23 2004
%N A006468 Number of rooted planar maps.
%F A006469 G.f.: (10+9x-3x^2)/(1-x)^7 (conjectured). - Ralf Stephan, Apr 23 2004
%N A006469 Number of rooted planar maps.
%N A006490 Generalized Lucas numbers.
%F A006490 Seems to be a(2) = 0, a(n) = n * A000045(n-1). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 01 2003
%N A006582 Sum k XOR n-k, k = 1 . . n-1.
%F A006582 a(0)=a(1)=0, a(2n) = 2a(n)+2a(n-1)+4n-4, a(2n+1) = 4a(n)+6n (conjectured). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 09 2003
%F A006697 G.f.: 1 + 1/(1-x) + 1/(1-x)^2 * [1/(1-x) - sum(k>=1, x^(2^k+k-1))] (conjectured). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 05 2004
%N A006697 Subwords of length n in word generated by a -> aab, b -> b.
%C A006965 Apparently a(n) = A038060(n)/3. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 01 2004
%N A006965 Number of directed trees with n nodes.
%F A007008 Appears to have A000346 as bisection. - R. Stephan, May 03 2004
%N A007008 Chvatal conjecture for radius of graph of maximal intersecting sets.
%N A007415 Expand sin x / exp x = x-x^2+x^3/3-x^5/30+... and invert nonzero coefficients.
%F A007415 a(n) = [n mod 4 > 0] * (-1)^(n+1+[n/4]) * n!/2^[n/2] (checked up to n=1000). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 06 2004
%N A007452 Expand cos x / exp x and invert nonzero coefficients.
%F A007452 a(4n+2) = 0, a(n) = (-1)^[n == 1,4,7 mod 8] * n!/2^floor(n/2) (checked up to n=1000). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 06 2004
%F A007476 G.f.: Sum{k=0..inf, x^(2k)/[prod(m=0..k-1, 1-mx)*prod(m=0..k+1, 1-mx)]} (conjectured). - R. Stephan, Apr 24 2004
%N A007476 Shifts 2 places left under binomial transform.
%N A007887 Fibonacci(n) mod 9.
%F A007887 a(n) has period 24. Proof: F_{n+24} = F_n + 9*(5152 F_{n+1} + 3184 F_n). - Olivier Wittenberg, following a conjecture by Ralf Stephan, Sep 28 2004
%N A009775 Expansion of tanh(ln(1+x)).
%F A009775 a(0) = 0, a(4n+3) = 0, a(n) = (-1)^[n == 2,5,8 mod 8] * n!/2^floor(n/2) (checked up to n=1000). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 06 2004
%N A009866 Coordination sequence T1 for Zeolite Code AHT.
%F A009866 Second differences seem to be periodic. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 24 2003
%C A010048 Conjecture: polynomials with (positive) Fibonomial coefficients are reducible iff n odd >1. - Ralf Stephan, Oct 29 2004
%N A010048 Triangle of Fibonomial coefficients.
%C A013525 Conjecture: for n>0, a(n) = 1/2 * (A000364(n) - 1). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 30 2004
%N A013525 arctanh(cosec(x)-cotan(x))=x+2/5!*x^5+30/7!*x^7+692/9!*x^9...
%N A013699 Degree of variety K_{2,n}^2.
%C A013699 It seems that a(n) = number of Catalan paths (nonnegative, starting and ending at 0, step +/-1) of 4n+4 steps with all values less than or equal to n+1 (see A080934). - Ralf Stephan (ralf(AT)ark.in-berlin.de), May 13 2003
%N A013701 Degree of variety K_{2,n}^4.
%C A013701 It seems that a(n) = number of Catalan paths (nonnegative, starting and ending at 0, step +/-1) of 6n+8 steps with all values less than or equal to n+1 (see A080934). - Ralf Stephan (ralf(AT)ark.in-berlin.de), May 13 2003
%C A018188 Numbers so far are all 11 mod 24. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 07 2003
%N A018188 The $620 prime list.
%N A020330 Numbers n such that base 2 representation is the juxtaposition of two identical strings.
%F A020330 a(2n) = 4a(n)-2n, a(2n+1) = 4a(n)-2n+2^[log2(4n+2)]+1 (conjectured). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 08 2003
%N A020479 Noninvertible 2 X 2 matrices over Z(n) (determinant is a divisor of 0).
%F A020479 a(n) seems to be divisible by n. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 01 2003
%F A020718 G.f.: (-4x^5+x^4+x^3-3x^2-2x+6)/[(1-x)(1-x-x^2-x^5)] (conjectured). - R. Stephan, May 12 2004
%N A020718 Pisot sequences E(6,10), P(6,10).
%F A020746 G.f.: (-x^5+x^4-x^3+x^2-2x+3)/[(1-x)(1-2x-x^3-x^5)] (conjectured). - R. Stephan, May 12 2004
%N A020746 Pisot sequence T(3,7).
%F A020748 G.f.: (-3x^5+2x^4+x^3-x^2-2x+4)/[(1-x)(1-2x-x^2-2x^5)] (conjectured). - R. Stephan, May 12 2004
%N A020748 Pisot sequence T(4,10).
%F A020957 For n>1, a(n) = [8*Lucas(n+1)-2n-5+(-1)^n]/4. G.f.: x(x^5+x^4-4x^2+3)/[(1-x)(1-x^2)(1-x-x^2)] (all conjectured). - R. Stephan, May 12 2004
%N A020957 Sum of [ 2*tau^(n-k) ] for k from 1 to infinity.
%F A021008 G.f.: (2x^3+x^2-4x+5)/(-x^4+2x^2-3x+1) (conjectured). - R. Stephan, May 12 2004
%N A021008 Pisot sequence P(5,11), a(0)=5, a(1)=11, a(n+1) is the nearest integer to a(n)^2/a(n-1).
%F A021011 G.f.: (3x^5+2x^4+x^3+4x^2-x+6)/(-x^6-x^3+x^2-2x+1) (conjectured). - R. Stephan, May 12 2004
%N A021011 Pisot sequence P(6,11), a(0)=6, a(1)=11, a(n+1) is the nearest integer to a(n)^2/a(n-1).
%F A022445 G.f.: [ -6x^7+10x^6-18x^5+27x^4-14x^3+10x^2-4x+1]/[(1+x^2)^2(1-2x)^2] (conjectured). - Ralf Stephan, Apr 28 2004
%N A022445 Number of self-avoiding closed walks (from 0 to 0) of length 2n in the strip {0, 1, 2} X Z of the square lattice Z X Z.
%N A022905 a(n) = M(n) + m(n) for n >= 2, where M(n) = max{ a(i) + a(n-i): i = 1..n-1 }, m(n) = min{ a(i) + a(n-i): i = 1..n-1 }.
%F A022905 a(n) = n + sum(k=2, n, A022907(n)) (conjectured). - Ralf Stephan, Feb 21 2004
%N A022907 The sequence m(n) in A022905.
%F A022907 a(n) = 3 * A033485(n-1) - 1 = 3/2 * A000123(n-1) - 1, n>1 (conjectured). - Ralf Stephan, Feb 21 2004
%N A022908 The sequence M(n) in A022905.
%F A022908 a(n) = n + sum(k=1, n-1, A022907(n)), n>1 (conjectured). - Ralf Stephan, Feb 21 2004
%C A023917 Presumably this is the same as A072837? - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 01, 2004
%N A023917 Theta series of A*_5 lattice.
%C A023919 Presumably this is the same as A072838? - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 01, 2004
%N A023919 Theta series of A*_7 lattice.
%F A026126 Apparently the second differences of A005325. - R. Stephan, Apr 06 2004
%N A026126 a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 5, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-4), where T is the array in A026120.
%F A026471 Numbers so far suggest that the first differences are 5-periodic. - R. Stephan, Apr 11 2004
%N A026471 a(n) = least positive integer > a(n-1) and not of the form a(i)+a(j)+a(k) for 1<=i<j<k<=n.
%N A026472 a(n) = least positive integer > a(n-1) and not a(i)+a(j)+a(k) for 1<=i<=j<=k<=n.
%F A026472 {3, 7} and congruent to {1, 2} mod 12 (conjectured). - R. Stephan, May 12 2004
%F A026476 For n>3, a(n) = 7n - 21 + 2(-1)^n (conjectured). - R. Stephan, Apr 30 2004
%N A026476 a(n) = least positive integer > a(n-1) and not a(i)+a(j)+a(k) for 1<=i<=j<=k<=n.
%F A026581 G.f.: (1+2x)/(1-x-4x^2) (conjectured). - Ralf Stephan, Feb 04 2004
%N A026581 T(n,0) + T(n,1) + ... + T(n,2n), T given by A026568.
%F A026583 G.f.: (1+2x)/[(1-x)(1-x-4x^2)] (conjectured). - Ralf Stephan, Feb 04 2004
%N A026583 a(n) = SUM{T(i,j)}, 0<=j<=i, 0<=i<=2n, T given by A026568.
%F A026597 G.f.: (1+x)/(1-x-4x^2) (conjectured). - Ralf Stephan, Feb 04 2004
%N A026597 T(n,0) + T(n,1) + ... + T(n,2n), T given by A026584.
%F A026599 G.f.: (1+x)/[(1-x)(1-x-4x^2)] (conjectured). - Ralf Stephan, Feb 04 2004
%N A026599 a(n) = SUM{T(i,j)}, 0<=j<=i, 0<=i<=2n, T given by A026584.
%F A026622 7 * 2^(n-2) - 2, a(0) = 1, a(1) = 2 (conjectured). Cf. A026624. - Ralf Stephan, Feb 05 2004
%N A026622 T(n,0) + T(n,1) + ... + T(n,n), T given by A026615.
%F A026624 G.f.: (1-x+x^2+x^3)/[(1-x)^2*(1-2x)] (conjectured). Cf. A026622. - Ralf Stephan, Feb 05 2004
%N A026624 a(n) = SUM{T(i,j)}, 0<=i<=n, 0<=j<=n, T given by A026615.
%F A026674 G.f.: 1/2*[(1-x)/(sqrt(1-4x)-x)-1] (conjectured). - Ralf Stephan, Feb 05 2004
%N A026674 a(n) = T(2n-1,n-1) = T(2n,n+1), T given by A026725.
%F A026945 a(n) = A005043(2n) + A005043(2n+1) (conjectured). - Ralf Stephan, Feb 06 2004
%N A026945 a(n) = sum of the squares of numbers in row n of array T given by A026300.
%F A027178 9*2^n - 4n - 8 (conjectured). - R. Stephan, Feb 13 2004
%N A027178 a(n) = T(n,0) + T(n,1) + ... + (T(n,n), T given by A027170.
%F A027181 G.f.: (1+x^2)/[(1-x)^2*(1-x-x^2)] (conjectured). - Ralf Stephan, Feb 16 2004
%N A027181 Lucas(n+4) - (2n+6).
%F A027261 2(n+1)*3^(n-1), for n>1 (conjectured). - Ralf Stephan, Feb 02 2004.
%N A027261 a(n) = SUM{(k+1)*T(n,k)}, 0<=k<=2n, T given by A025177.
%N A027615 Number of 1's when n is written in base -2.
%F A027615 a(n) = 3 * A072894(n+1) - 2n - 3. Proof by Nikolaus Meyberg, following a conjecture by Ralf Stephan.
%F A027950 G.f.: [x^2(1-2x+41x^2-49x^3+44x^4-26x^5+8x^6-x^7)]/[(1-3x+x^2)(1-x)^5] (conjectured). - R. Stephan, Apr 24 2004
%N A027950 T(2n,n+2), T given by A027948.
%F A027992 Conjectures: a(n) = 2^n*(3n-1)+2 = A048496(n+1)-1 = A053565(n+1)+2. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 15 2004
%N A027992 a(n) = 1*T(n,0) + 2*T(n,1) + ... + (2n+1)*T(n,2n), T given by A027926.
%F A028403 Appears to be 2*A007582(n-1). - R. Stephan, Mar 24 2004
%N A028403 Number of types of Boolean functions of n variables under a certain group.
%N A032058 "BGK" (reversible, element, unlabeled) transform of 1,1,1,1...
%F A032058 Numbers so far satisfy a(n) = 1/2 * (A032020(n)+1). - Ralf Stephan, Apr 06 2004
%F A032087 Conjecture: a(2n+1) = 2^(4n+1) - 2^(2n+1), a(2n) = 2^(4n-1) - 2^(2n) + 2^(2n-1), a(1)=4. - Ralf Stephan, Mar 25 2004
%N A032087 Number of reversible strings with n beads of 4 colors. If more than 1 bead, not palindromic.
%N A032091 Number of reversible strings with n-1 beads of 2 colors. 4 beads are black. String is not palindromic.
%F A032091 Numbers so far suggest that a(n+6) = 2*A002624(n). - R. Stephan, Mar 31 2004
%N A032098 "BHK" (reversible, identity, unlabeled) transform of 3,3,3,3...
%F A032098 Conjecture: a(n) = 3 * (2^(2n-3) - 2^(n-2) + 1). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 11 2003
%N A032106 Number of reversible strings with n black beads and n-1 white beads. String is not palindromic.
%F A032106 a(2n) = 1/4 * [C(4n,2n) - C(2n,n)], a(2n+1) = A034872(4n+2)-A034872(4n+1) (conjectured). - R. Stephan, May 04 2004
%N A032112 "BIJ" (reversible, indistinct, labeled) transform of 2,1,1,1...
%F A032112 Numbers so far suggest that a(n) = (A006155(n)+1)/2. - Ralf Stephan, Mar 12 2004
%N A032170 "CHK" (necklace, identity, unlabeled) transform of 1,2,3,4...
%C A032170 Apparently, for n>2, the same as A072337. - R. Stephan, Feb 01 2004
%F A032191 G.f.: [1-x+x^2+4x^3+2x^4+3x^6+x^7+x^8]/[(1-x)^6(1+x)^3(1+x+x^2)^2(1-x+x^2)] (conjectured). - R. Stephan, May 05 2004
%N A032191 Number of necklaces of n beads of 2 colors, 6 of them black.
%N A033157 Begins with (1, 4); avoids 3-term arithmetic progressions.
%F A033157 Seems to equal A004793(n) + [n is even] + [ceiling(n/2) is even]. - Ralf Stephan, Apr 06 2004
%F A033441 G.f.: x[1/(1-x) - 1/(1-x^9)]/(1-x)^2 (conjectured). - R. Stephan, Mar 05 2004
%N A033441 Number of edges in 9-partite Turan graph of order n.
%F A034184 Appears to obey a 9-term linear recurrence. - R. Stephan, May 05 2004
%N A034184 Not necessarily symmetric n x 3 crossword puzzle grids.
%F A034702 For n>2: a(n)=b(n+2), with b(0)=0, b(2n)=2b(n)+3, b(2n+1)=2b(n)+6-8[n==0]; a(n)=3n+3-2*2^[log2(n+2)] (conjectured). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 23 2004
%N A034702 a(n+1) is the smallest number not of the form a(i), a(i)+a(n-1), or |a(i)-a(n-1)|.
%F A035487 It appears that a(n+1) = A001965(n)+2+3n = A001966(n)+n. - Ralf Stephan, Feb 24 2004
%N A035487 Second column of Stolarsky array.
%F A035612 Conjecture: a(n) = v2(A022340(n)), where v2(n) = A007814(n), the dyadic valuation of n. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jun 20 2004
%N A035612 Horizontal para-Fibonacci sequence: says which column of Wythoff array (starting column count at 1) contains n.
%F A035615 G.f.: x(2x^6-6x^5+8x^4+2x^3-6x^2+2x)/[(1-x^2)(1-2x)(1-x-x^2)^2] (conjectured). - R. Stephan, May 11 2004
%N A035615 Number of winning n-digit binary strings in "same game".
%N A036258 Number of inequivalent strings of n digits, when 2 strings are equivalent if turning 1 upside down gives the other.
%F A036258 a(n+1) = (1/10)*{10^n - 5^n + (4-(-1)^n)*5^[n/2]} (conjectured). - R. Stephan, May 11 2004
%F A036583 Numbers so far suggest that a(n) = A036581(n)+1. - R. Stephan, Apr 19 2004
%N A036583 Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.
%C A037412 Appears to be a subset of A033044. - R. Stephan, Aug 18 2004
%N A037412 n-th number k such that the set of base 2 digits of k equals the set of base 7 digits of k.
%C A038060 Apparently, for n>0, a(n) = 3 * A006965(n). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 01 2004
%N A038060 Number of trees with 3-colored nodes.
%N A038552 Conjectured value of largest squarefree number k such that Q(sqrt(-k)) has class number n.
%C A038552 Numbers so far are all 19 mod 24. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 07 2003
%N A038554 Derivative of n: write n in binary, replace each pair of adjacent bits by their mod 2 sum (a(0)=a(1)=0 by convention). Also n XOR (n shift 1).
%F A038554 a(0) = a(1) = 0, a(4n) = 2a(2n), a(4n+2) = 2a(2n+1)+1, a(4n+1) = 2a(2n)+1, a(4n+3) = 2a(2n+1). Proof by Nikolaus Meyberg following a conjecture by Ralf Stephan.
%F A039823 G.f.: x(x^4-2x^3+2x^2-x+1)/[(1+x^2)(1-x)^3] (conjectured). - R. Stephan, May 11 2004
%N A039823 Number of different coefficient values in expansion of Product (1+q^1+...+q^i), i=1 to n.
%C A039824 Conjecture: for n>6, a(n) = n^2 - 3. - R. Stephan, Mar 07 2004
%N A039824 Number of different coefficient values in expansion of Product (1+q^1+q^3...+q^(2i-1)), i=1 to n.
%N A045626 Bends in loxodromic sequence of spheres in which each 5 consecutive spheres are in mutual contact.
%F A045626 G.f.: [ -2x^4-x^3+2x^2+3x-1]/[(1+x)(1-2x+x^2-2x^3+x^4)] (conjectured). - R. Stephan, May 06 2004
%N A045668 2n-bead balanced binary strings of fundamental period 2n, rotationally equivalent to complement, inequivalent to reverse and reversed complement.
%F A045668 It seems that a(n) = 4*n*A011948(n). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 30 2003
%F A047837 Appears to obey a 16-term linear recurrence. - R. Stephan, May 06 2004
%N A047837 Honaker's triangle problem: form a triangle with base of length n, all entries different, all row sums equal; a(n) gives minimal row sum.
%C A049053 Numbers so far are all 5 mod 16. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 07 2003
%N A049053 n through n+6 all have same number of divisors
%C A051283 A080170(n+1) + 1 (conjectured). - Ralf Stephan, Feb 20 2004
%N A051283 Numbers n such that if write n = Product p_i^e_i (p_i primes), and P = max p_i^e_i, then n/P > P.
%C A054096 Conjecture: sequence is A006183 shifted right. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 15 2004
%N A054096 T(n,2), array T as in A054090.
%F A055278 G.f.: x^4(x^3+x^2+1)/[(1-x^2)(1-x^3)(1-x)^3] (conjectured). - Ralf Stephan, Mar 07 2004
%N A055278 Number of rooted trees with n nodes and 3 leaves.
%C A055414 Numbers so far are all 1 mod 16. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 07 2003
%N A055414 Points in Z^8 of norm <= n.
%F A055418 Appears to satisfy a 9-degree polynomial. - Ralf Stephan, Mar 07 2004
%N A055418 Points in N^n of norm <= 3.
%F A055427 Appears to satisfy a 9-degree polynomial. - Ralf Stephan, Mar 07 2004
%N A055427 Points in Z^n of norm <= 3.
%C A056739 It appears that the sequence contains A003598. - R. Stephan, Aug 16 2004
%N A056739 Numbers n such that n | 10^n + 9^n + 8^n + 7^n + 6^n + 5^n + 4^n + 3^n + 2^n + 1^n.
%N A056777 Composite n such that both Phi(n+12)=Phi(n)+12 and Sigma(n+12)=Sigma(n)+12.
%C A056777 Numbers so far are all 65 mod 72. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 07 2003
%N A057300 Binary counter with odd/even bit positions swapped; base 4 counter with 1's replaced by 2's and vice versa.
%F A057300 a(2n) = -2a(n) + 5n, a(2n+1) = -2a(n) + 5n + 2 (conjectured). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 11 2003
%F A057349 Is a(n) = A083033(n-1) + n + 2? - Ralf Stephan, Feb 24 2004
%N A057349 Leap years in the Hebrew Calendar starting in year 1 (3761 BCE). The leap year has an extra -month-.
%F A057870 Appears to satisfy a 13-term linear recurrence. - Ralf Stephan, Mar 07 2004
%N A057870 Number of singular points on n-th order Chmutov surface.
%F A059158 (24/7) * (8*16^n - 2^n) (conjectured). - R. Stephan, May 05 2004
%N A059158 A hierarchical sequence (S(W'3{2,2}cc) - see A059126).
%F A059816 Apparently, for n>8, a(2n) = 2n-1, a(2n+1) = n. - R. Stephan, May 29 2004
%N A059816 Let g_n be ball packing n-width for torus X square; sequence gives denominator of (g_n/Pi)^2.
%N A060621 Number of flips between the d-dimensional tilings of the unary zonotope Z(D,d). Here the codimension D-d is equal to 3 and d varies.
%F A060621 Numbers so far satisfy a(n) = 2^n*(n^2+11n+24)/2. - R. Stephan, Apr 08 2004
%F A062730 G.f.: (-5x^8+3x^7+7x^6-3x^5+5x^4-5x^3-12x^2+5x+7)/[(1-x)(1-x^2)^2] (conjectured). - R. Stephan, May 08 2004
%N A062730 Rows of Pascal's triangle which contain 3 terms in arithmetic progression.
%N A062854 First differences of A027424.
%F A062854 It appears that a(n) = A061228(n)/2 unless n is a member of A066423. - Ralf Stephan, Mar 02 2004
%N A063221 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 57 ).
%F A063221 Seems to be 6n - 3 + A062157(n-1). - Ralf Stephan, Feb 16 2004
%N A063797 Numbers n such that sigma(d(n^3))==d(sigma(n^2)), where d(n) is the number of divisors of n.
%C A063797 Numbers so far are all 1 mod 24. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 07 2003
%N A063880 Numbers n such that sigma(n) = 2*usigma(n).
%C A063880 Numbers so far are all == 108 mod 216. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 07 2003. Confirmed up to 10^7 by Robert G. Wilson v.
%F A063920 G.f.: (10 + 14x)/(1 - 2x^2) (conjectured). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 19 2004
%N A063920 t(n) = z(n) where t(n)= |eulerphi(n)-n| and z(n)= t(t(n)-n).
%C A064433 Appears to have the same parity as A006666. - R. Stephan, Sep 01 2004
%N A064433 Number of iterations of A064455 to reach 2 (or 1 in the case of 1).
%N A065304 Numbers n such that A003285(n) = A003285(n+1).
%C A065304 Numbers so far are all 1 mod 24. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 07 2003
%N A065359 Alternating bit sum for n: replace 2^k with (-1)^k in binary expansion of n.
%C A065359 Conjectures: a(n) = 3 or -3 iff n in 3*A036556; a(n) = 0 iff n=3k with k not in A036556. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 07 2003
%F A065450 Conjectures: G.f.: [1+6x^2+4x^3-4x^4-2x^5+2x^6]/[(1+x)*(1-x)^3]. For n>3, partial sums of A047356. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 06 2004
%N A065450 Make an infinite chessboard from the squares in the first quadrant; sequence gives number of squares a knight can reach in n moves starting at the origin.
%C A065558 Conjecture: a(2n) = 2*A001615(n). - R. Stephan, Mar 26 2004
%N A065558 Let G_n be the group of invertible 2 X 2 matrices mod n (sequence A000252). a(n) is the maximal degree of an irreducible representation of G_n.
%N A067348 Central binomial coefficient C(n,n/2) is divisible by n.
%C A067348 Conjecture: sequence contains most of 2*A000384(k). Exceptions are k=8,18,20,23,35,... - R. Stephan, Mar 15 2004
%N A067720 Numbers n such that phi(n^2+1)=n*phi(n+1).
%C A067720 Superset of A070689. Is a(5)=8 the only additional value? - Ralf Stephan, Feb 11 2004
%C A069187 Conjecture: sequence is A071253 minus those entries of A071253 that have their index in A049532, i.e. a(n) is of form n^2*(n^2+1) for all n not in A049532. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 18 2004
%N A069187 Numbers n such that core(n)=ceil(sqrt(n)) where core(x) is the square-free part of x (the smallest integer such that x*core(x) is a square).
%F A069306 G.f. x^2(2x+5)/(1-2x-x^2) (conjectured). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 16 2004
%N A069306 Number of 2 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.
%F A070263 Rows seem to converge to expansion of 1/(1-x)^2 * sum(k>=0, 2^kt/(1-t^2), t=x^2^k). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 12 2003
%N A070263 Triangle T(n,k), n>=0, 1 <= k <= 2^n, read by rows, giving minimal distance-sum of any set of k binary vectors of length n.
%F A070814 For n>10, a(n) = 2a(n-4) (conjectured). - R. Stephan, May 09 2004
%N A070814 Solutions to Phi[P[x]]-P[Phi[x]]=14=c are special multiples of 17, x=17k, where largest prime factors of factor k were observed from {2, 3, 5}, i.e. it is smaller than 17. See solutions to other even cases of c [=A070813]: A007283 for 0, A070004 for 2, A070815 for 254, A070816 for 65534.
%N A071052 Number of 0's in n-th row of triangle in A071036.
%F A071052 a(2n) = a(n) + 2n (conjectured). - Ralf Stephan, Mar 03 2004
%N A071055 Number of 0's in n-th row of triangle in A071038.
%F A071055 a(n)=b(n+1), with b(0)=0, b(2n)=b(n), b(2n+1)=2b(n)+2-2[n==0] (conjectured). - Ralf Stephan, Mar 05 2004
%F A071721 6n * (2n)! / [(n+2)n!(n+1)!)], n>0 (confirmed up to n=1000). In terms of Catalan numbers (A000108), a(n) = 6n*Cat(n)/(n+2). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 11 2004
%N A071721 Expansion of (1+x^2*C^2)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
%F A072206 Numbers so far, except 2, satisfy a(n) = 1 + k/3 * (4k^2+5), with k apparently in A005097. - Ralf Stephan, Aug 21 2004
%N A072206 Third terms of triple Peano sequence A071988.
%F A072222 For n>6, a(n) = a(n-3) + 2 (conjectured). - R. Stephan, May 09 2004
%N A072222 a(n) = mod(abs(n-1-a(n-2)],n) + mod(abs(n-1-a(n-1)],n-1], a(0) = 1, a(1) = 1.
%C A072337 Apparently, for n>2 the same as A032170. - R. Stephan, Feb 01 2004
%N A072337 Inverse EULER transform of A064831 (with its initial 1 omitted).
%C A072493 Is this sequence, with its first 8 terms removed, the same as A005427? See also the similar conjecture with A005428/A073941. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 04 2003
%N A072493 a(1)=1, a(n)=ceiling((sum_{k=1..n-1} a(k))/3).
%N A072837 Expansion of F_6(q^2).
%C A072837 Presumably this is the same as A023917? - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 01, 2004
%N A072838 Expansion of F_8(q^2).
%C A072838 Presumably this is the same as A023919? - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 01, 2004
%N A074355 Coefficient of q^1 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=b*nu(n-1)+lambda*(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,3).
%F A074355 G.f.: (9x^4+3x^3)/(1-3x-3x^2)^2 (conjectured). - R. Stephan, May 09 2004
%F A075123 G.f.: [1+x-3x^2+2x^3+5x^4+3x^6]/[(1+x)(1-x)^2] (conjectured). - R. Stephan, Feb 14 2004
%N A075123 a(n) = least positive integer > a(n-1) and not 2*a(i)+a(j) for 1<=i<j<n.
%F A075249 Is a(n) = A047252(n-3)-n+4 ? - Ralf Stephan, Feb 24 2004
%N A075249 x-value of the solution (x,y,z) to 5/n = 1/x + 1/y + 1/z satisfying 0 < x < y < z and having the largest z-value. The y and z components are in A075250 and A075251.
%N A075530 Number of consecutive integers in the set of all possible values in a stochastic sequence.
%F A075530 Numbers so far suggest that a(n) = A003064(n) - n + 1, n>1. - R. Stephan, Mar 21 2004
%F A076178 Conjecture: a(n) = 2 * A078903(n). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 23 2003
%N A076178 a(n)=2*n^2-A077071(n).
%N A076182 A006666(n) mod 2.
%F A076182 Apparently also the parity of A064433. - Ralf Stephan, Feb 24 2004
%N A076274 2p-1 where p is 1 or a prime.
%F A076274 Appears to equal A083251(n+1)/8 - 1 for n>2. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 05 2003
%N A076505 3 people at a party are saying Hello to each other. Person 1 says Hello. Person 2 counts the times Hello has been said, and says Hello twice that number. Person 3 says Hello 3 times the sum of Hello's, and then it's Person 1 again. This is how many Hello's each person says.
%F A076505 Conjecture: a(n) = 2^i*3^j, with i=A064429(n-1), j=[n/3]+[n%3==0]. - R. Stephan, Mar 16 2004
%N A076984 Number of Fibonacci numbers that divide the n-th Fibonacci number.
%F A076984 a(n) = tau(n)-[n is even] = A000005(n)-A059841(n). Proof: gcd(Fib(m),Fib(n)) = Fib(gcd(m,n)) and Fib(2) = 1. - Olivier Wittenberg, following a conjecture by Ralf Stephan, Sep 28 2004
%F A078489 Conjecture: a(n) = A003258(n) - n + 1. - Ralf Stephan, Feb 24 2004
%N A078489 a(n)=j such that binomial(n,j)<binomial(n-1,j-2).
%N A078700 Number of symmetric ways to lace a shoe that has n pairs of eyelets such that each eyelet has at least one direct connection to the opposite side.
%F A078700 Numbers so far satisfy a(n) = Sum[k=0..n, k!*C(k,n)*Fibonacci(k+2)]. - R. Stephan, May 23 2004
%F A078903 Conjecture: a(n) = 1/2 * A076178(n). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 23 2003
%N A078903 a(n)=n^2-sum(u=1,n,sum(v=1,u,valuation(2*v,2))).
%C A079670 The members of the sequence seem to be all integers. Conjecture: a(n)>1 if A080050(n) not equivalent 1 (mod 10). The reverse is not true.
%N A079670 a(n) = (GCD(2^p-1,Fibonacci(p))-1)/(8p) > 0 where p = n-th prime from A080050.
%N A080050 Primes p such that 2^p-1 and the p-th Fibonacci number have a common factor. Prime members of A074776.
%C A080050 The sequence is a subset of A074776. Conjecture: all multiples k*p of this sequence are in A074776, i.e. they satisfy gcd(2^(kp)-1,fibonacci(kp)) > 1.
%C A080170 A051283(n-1) - 1 (conjectured). - Ralf Stephan, Feb 20 2004
%N A080170 Numbers n such that GCD(C(2*n,n), C(3*n,n), C(4*n,n) ..., C((n+1)*n,n) ) = 1.
%N A080572 Number of ordered pairs (i,j), 0 <= i,j < n, for which (i & j) is nonzero, where & is the bitwise AND operator.
%F A080572 a(0)=a(1)=0, a(2n) = 3a(n)+n^2, a(2n+1) = a(n)+2a(n+1)+n^2-1 (conjectured). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 07 2003
%N A080795 Number of minimax trees.
%F A080795 a(2n) = 2^n * A006154(2n), n>0 (conjectured). - R. Stephan, Apr 29 2004
%N A081504 Numbers n such that there are no primes of the form 2^n+2^i+1, 0<i<n. In binary: all 3-bit numbers with size n+1 are composite.
%C A081504 There seem to be no such numbers (bit sizes) such that any 4- or 5-bit number is composite, up to n around 200.
%C A082022 Conjectures: if n is even and n+1 is prime, a(n) = n^2 * (n-1)!^2. If n is odd and >3, 2*(n+1)*a(n) is a perfect square, the root of which has the factor 1/2*n*(n-1)*((n-1)/2)!. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 08 2003
%N A082022 In the following square array a(i,j) = Least Common Multiple of i and j. Sequence contains the product of the terms of the n-th antidiagonal.
%N A082184 The a(n)-th triangular number is the sum of the n-th triangular number and the smallest triangular number possible.
%C A082184 a(n) is triangular if n+1 is triangular. Conjectures: partial maxima of sequence are at index i with value from A068195, and also a(i)-A082183(i)=1, where i is in A068194.
%F A082630 Apparently a(n)a(n+3) = -2 + a(n+1)a(n+2). - R. Stephan, May 29 2004
%N A082630 Start with the sequence S(0)={1,1} and for n>0 define S(n) to be I(S(n-1)) where I denotes the operation of inserting, for i=1,2,3..., the term a(i)+a(i+1) between any two terms for which 7a(i+1)<=11a(i). The listed terms are the initial terms of the limit of this process.
%C A082635 It seems that T(n,2i) = A080934((i+1)n+2i,n+1).
%N A082635 Square array read by antidiagonals: degree of the K(2,p)^q variety.
%F A082909 Is this A070940 shifted left? - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 06 2003
%N A082909 a(n) is the number of distinct values of GCD[2^n,C[n,j]] arising if j=0,..,n-1.
%F A083251 Appears to equal 8 * (A076274(n-1)+1) for n>3. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 05 2003
%N A083251 Numbers n for which Abs[A045763[n]-A073757[n]]=2, i.e. signed difference of size of related and unrelated sets to n equals either 2 or -2.
%C A083866 First differences seem to be always >2.
%N A083866 Positions of zeros in Per Noergaard's infinity sequence (A004718).
%C A083905 Conjecture: a(3*A006288) = 0.
%N A083905 G.f.: 1/(1-x) * sum(k>=0, (-1)^k*x^2^(k+1)/(1+x^2^k)).
%C A084087 Conjecture: a(n) are all positions of nonzero coefficients in expansion of sum(k>=0, x^2^k/(1+x^2^k+x^2^(k+1))) (A084091).
%C A084087 It seems that lim(n->inf, a(n)/n) = 9/4.
%N A084087 Not divisible by 3 and exponent of highest power of 2 dividing a(n) is even.
%C A084088 Conjecture: a(n) are all positions of -1 in expansion of sum(k>=0, x^2^k/(1+x^2^k+x^2^(k+1))) (A084091).
%C A084088 It seems that lim(n->inf, a(n)/n) = 9/2.
%N A084088 a(n) = 2 mod 3 and exponent of highest power of 2 dividing a(n) is even.
%C A084089 Conjecture: a(n) are all positions of +1 in expansion of sum(k>=0, x^2^k/(1+x^2^k+x^2^(k+1))) (A084091).
%C A084089 It seems that lim(n->inf, a(n)/n) = 9/2.
%N A084089 a(n) = 1 mod 3 and exponent of highest power of 2 dividing a(n) is even.
%C A084090 Conjecture: a(n) are all positions of 0 in expansion of sum(k>=0, x^2^k/(1+x^2^k+x^2^(k+1))) (A084091).
%N A084090 Divisible by 3 or exponent of highest power of 2 dividing a(n) is odd. Complement of A084087.
%C A084090 It seems that lim(n->inf, a(n)/n) = 9/5.
%N A084091 Expansion of sum(k>=0, x^2^k/(1+x^2^k+x^2^(k+1))).
%Y A084091 Positions of 0 seem to be in A084090, of 1 in A084089, of -1 in A084088, of a(n)!=0 in A084087.
%N A084391 For n>3, a(n) = smallest number divisible by exactly n-2 previous terms; a(n)=n for n<=3.
%F A084391 G.f. [x * (6x^6-6x^5-4x^3-3x^2-2x-1)]/(1-6x^4) (conjectured). - Ralf Stephan, Feb 03 2004
%C A084889 Any member of A000404 is in sequence, since if a = x^2 + y^2, then a^3 = (ax)^2 + (ay)^2. But is the reverse true? - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 16 2003
%N A084889 Numbers whose cubes can be partitioned into two squares>0.
%F A085348 Apparently a(n)a(n+3) = -4 + a(n+1)a(n+2). - R. Stephan, May 29 2004
%N A085348 Ratio-determined insertion sequence I(0.264) (see the link below).
%F A085349 Apparently a(n)a(n+3) = 11 + a(n+1)a(n+2). - R. Stephan, May 29 2004
%N A085349 Ratio-determined insertion sequence I(0.26688) (see the link below).
%F A085376 Apparently a(n)a(n+3) = -3 + a(n+1)a(n+2). - R. Stephan, May 29 2004
%N A085376 Ratio-dependent insertion sequence I(0.36704) (see the link below).
%C A085765 Conjecture: a(n) mod 2 repeats the 7-pattern 0,0,1,1,1,0,1.
%C A085765 Conjecture: log(a(n))/log(n) grows unboundedly.
%N A085765 Partial sums and bisection of A086450.
%N A086372 First differences of A027349.
%C A086372 Sequence seems to have the same parity as A000041, the partition numbers, i.e. a(n) is congruent A040051(n) mod 2.
%C A086449 Apparently a(n) = number of ways of writing n as a sum of powers of 2, where each power appears p times, with p itself a power of 2.
%C A086449 Conjectures: all a(n) are even except a(2^k-1) = 1. Also a(2^k-2) = 2^(k-1).
%N A086449 a(0) = 1, a(2n+1) = a(n), a(2n) = a(n) + a(n-1) +...+ a(n-2^m) +...where a(n<0) = 0.
%C A086450 Conjecture: a(n) mod 2 repeats the 7-pattern 1,1,0,1,0,0,1 (A011657).
%N A086450 a(0) = 1, a(2n+1) = a(n), a(2n) = a(n) + a(n-1) +...+ a(n-m) +... where a(n<0) = 0.
%N A087097 Dismal primes (cf. A087062).
%C A087097 Is this the same as A088474? - Ralf Stephan, Mar 06 2004
%N A087719 Least number m such that the number of numbers k<=m with k>spf(k)^n exceeds the number of numbers with k<=spf(k)^n.
%F A087719 Numbers so far satisfy a(n) = 3^n + 3*2^n + 6. - R. Stephan, May 10 2004
%Y A087808 A048678(k) is where k appears first in sequence.
%N A087808 a(0) = 0; a(2n) = 2a(n), a(2n+1) = a(n) + 1.
%C A088474 Is this the same as A087097? - Ralf Stephan, Mar 06 2004
%N A088474 Numbers n such that dismal sum of prime divisors of n is = n
%C A089066 Is this the same as A099030? - R. Stephan, Sep 27 2004
%N A089066 Number of unique permutations of length n.
%N A089893 (A001317(2n)-1)/4.
%C A089893 Conjecture: a(2^k) = 2^(2^(k+1)-2).
%C A089893 Conjectures: lim(n->inf, a(2n+1)/a(2n)) = 5, lim(n->inf, a(4n+2)/a(4n+1)) = 17/5, lim(n->inf, a(8n+4)/a(8n+3)) = 257/85 etc.
%C A090681 Conjecture: a(n) = |A012670(n)/2^(6n+1)| = A012853(n)/2^(4n+1). - Ralf Stephan, Feb 06 2004
%N A090681 Expansion of (sec(x/2)^2+sech(x/2)^2)/2 in powers of x^4.
%C A091067 Conjecture: a(n) = A060833(n+1) - 1.
%N A091067 Odd part of n is of form 4k+3.
%F A091468 3*A003239(n) - 2 (conjectured). - Ralf Stephan, Feb 06 2004
%N A091468 Number of unlabeled alternating octupi with n black nodes and n white nodes.
%N A091817 (2*numerator(H(p-3)) -3*denominator(H(p-3)))/p with H(m) = 1 + 1/2 + 1/3 + ...+ 1/m.
%C A091817 Leroy Quet conjectures that the terms are always integral. This is true for p < 3*10^4.
%F A092482 For n>2, a(n+2) = 1 + 2^[log2(n)] + sum[k=1,n,(3^A007814(n)+1)/2] = 1 + A053644(n) + A005836(n) (conjectured and checked up to n=512).
%N A092482 Sequence contains no 3-term arithmetic progression, starting with "illegal" 1,2,3.
%N A093109 Numbers k such that the Zsigmondy number Zs(5,1,k) differs from the kth cyclotomic polynomial evaluated at 5.
%C A093109 Vladeta Jovovic points out that the sequence seems to contain the powers of two as well as the numbers of the form 3*2^k.
%F A093210 Conjecture: a(n) = A060477(n+4) - 2. - R. Stephan, Apr 24 2004
%N A093210 Row sums of A092964.
%N A093678 Sequence contains no 3-term arithmetic progression, starting with 1,7.
%F A093678 a(n) = sum[k=1,n-1,(3^A007814(k)+1)/2] + f(n), with f(n) an 8-periodic function with values {1,6,5,6,2,6,5,7,...}, n>=1 (conjectured and checked up to n=1000).
%N A093679 Sequence contains no 3-term arithmetic progression, starting with 1,10.
%F A093679 a(n) = sum[k=1,n-1,(3^A007814(k)+1)/2] + f(n), with f(n) an 8-periodic function with values {1,9,8,9,5,10,10,10,...}, n>=1 (conjectured and checked up to n=1000).
%N A093680 Sequence contains no 3-term arithmetic progression, starting with 1,19.
%F A093680 a(n) = sum[k=1,n-1,(3^A007814(k)+1)/2] + f(n), with f(n) a 16-periodic function with values {1,18,17,18,14,18,17,19,5,18,17,18,14,19,19,19,...}, n>=1 (conjectured and checked up to n=1000).
%N A093681 Sequence contains no 3-term arithmetic progression, starting with 1,28.
%F A093681 a(n) = sum[k=1,n-1,(3^A007814(k)+1)/2] + f(n), with f(n) a 16-periodic function with values {1,27,26,27,23,27,26,27,14,28,28,28,28,28,28,28,...}, n>=1 (conjectured and checked up to n=1000).
%N A093682 Array T(m,n) by antidiagonals: nonarithmetic-3-progression sequences with simple closed forms.
%F A093682 T(m,n) = sum[k=1,n-1,(3^A007814(k)+1)/2] + f(n), with f(n) a P-periodic function, where P <= 2^[(m+3)/2] (conjectured and checked up to m=13,n=1000).
%C A093682 The nonarithmetic-3-progression sequences starting with a(1)=1, a(2)=1+3^m or 1+2*3^m, m>=0, seem to have especially simple 'closed' forms. None of these formulas is proved, however, and readers are encouraged to do so.
%N A094424 Array read by antidiagonals: Solutions to Schmidt's Problem.
%Y A094424 Columns 2-3 seem to be A000079, A081656.
%N A094954 Array T(k,n) read by antidiagonals. G.f.: x(1-x)/(1-kx+x^2), k>1.
%H A094954 Elizabeth Wilmer, <a href="http://www.oberlin.edu/math/faculty/wilmer/OEISconj87.pdf">A note on Stephan's conjecture 87</a>
%C A095917 Can a(n) be expressed in terms of F(n), without the sum? However, the sequence appears not to be C-finite.
%N A095917 Unreduced numerator of Sum[k=1..n, -(-1)^k/(F(k)*F(k+1))], with F(i) = A000045(i) the Fibonacci numbers.
%N A096304 Numbers n such that 3n does not divide (6n-4)!/[(3n-2)!(3n-1)! ].
%F A096304 a(n) = 9 * A005836([n/6]) + (n mod 6) (conjectured).
%N A097322 (2n)! divided by denominator of Taylor expansion of exp(cos(x)-1).
%C A097322 Conjectures: a(n) is divisible by 4 for n = 2 mod 3; a(n) is divisible by 11 for n = 0 mod 5; a(n) is divisible by 29 for n>20 and n = 7,13 mod 14. More generally, prime factors dividing some a(n) are distributed periodically, with the set of primes starting {2,11,29,31,41,53,73,83,89,131,...}.
%N A097323 One sixth of the unitary sociable numbers.
%C A097323 We conjecture that a(n) is always an integer.
%N A097324 Numbers n such that A067655(n) is different from A049606(n).
%C A097324 We conjecture that the sequence is infinite, the sequence and its complement (cases where the two values are equal) equipartition N, and the difference between consecutive members of this sequence never exceeds c=7.
%N A097632 2^n * Lucas(n).
%F A097632 E.g.f.: -log(1-2x-4x^2). Contrary to b(n) = 2^n*Fib(n), there seems to be no rational o.g.f. for the sequence.
%C A097700 Is lim[n->inf, a(n)/n] = 3/4?
%N A097700 Numbers not of form x^2 + 2y^2.
%N A097702 (A063880(n) - 108)/216.
%C A097702 Conjecture: n is a member iff 6*n+3 is square-free. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 27 2004
%C A097702 It is only a conjecture that all terms are integers (confirmed up to 10^6 by Robert G. Wilson v).
%C A097703 Conjecture: all numbers of form 3k + 1 are here. Other terms are listed in A097704.
%N A097703 Numbers n such that m = 216n + 108 satisfies sigma(m) <> 2*usigma(m).
%C A097704 Conjecture: "most" of the terms also belong to [(A067778-1)/2]. Exceptions are {302, 2117, ...}. In other words, most terms satisfy: GCD(2n+1, numerator(B(4n+2))) is not squarefree, with B(n) the Bernoulli numbers.
%N A097704 Elements of A097703 not of form 3k + 1.
%C A098434 The Genocchi numbers A001489 appear as constant term of every second polynomial and as the negative sum of its coefficients.
%N A098434 Triangle read by rows: coefficients of Genocchi polynomials G(n,x); n times the Euler polynomials.
%C A099030 Is this the same as A089066?
%N A099030 Number of tone-rows in n-tone music.
%N A099173 Array T(k,n) read by diagonals: g.f. of k-th row x/(1-2x-(k-1)x^2).
%H A099173 R. Stephan, <a href="http://arXiv.org/abs/math.CO/0409509">Prove or disprove. 100 Conjectures from the OEIS</a>, #16.

Makefile:

conj: sauth names
	grep -h '%[FCY].*R.*Stephan' eisBTfry* | grep "onject\|ppear\|eem\|\?\|so far\|pparently\|onfirmed\|hecked" >conj.tmp1
	grep "onjecture\|ppear\|eem\|\?\|so far\|pparently\|onfirmed\|hecked" sauth >>conj.tmp1
	sort +1 conj.tmp1 >conj.tmp
	rm -f conj.tmp1
	for i in `cat conj.tmp|sed 's/%. \(A......\).*/\1/g'|uniq` ; do echo $$i ; grep "%N $$i" names >>conj.tmp1 ; done
	cat conj.t* | sort +1 >conj

sauth:
	grep -h '%A.*R.*Stephan' eisBTfry* |sort +1 >sauth.tmp
	wc sauth.tmp
	rm -f sauth
	for i in `cat sauth.tmp|sed 's/%. \(A......\).*/\1/g'|uniq` ; do echo $$i ; grep -h "%. $$i" eisBTfry* >>sauth ; done

names:
	grep -h '%N A' eisBTfry* >names

veclist:
	grep A09 stripped |sed "s/A00/vv\\[/g" | sed "s/ ,/\\]=\\[/g" | sed "s/,$$/\\]/g" |sed "s/A09/vv\\[/g"| sed "s/\\[0000\\]/\\[10000\\]/g" 

authors:
	grep -h '^%A A' eisBTfry* >authors

conj-all:
	grep -h '%[FCY]' eisBTfry* | grep "onjectur\|ppear\|[sS]eem\|\?\|so far\|pparently\|onfirmed\|hecked" >conj-all

tabs:
	grep -h '%K.*tab' eisBTfry* >tabs 

tabllist: tabs
	rm -f tabllist
	for i in `cat tabs|grep tabl|sed 's/%. \(A......\).*/\1/g'|sort|uniq` ; do echo $$i ; grep -h "%. $$i" eisBTfry* >>tabllist ; done

nicebaselist: nicebase
	rm -f nicebaselist
	for i in `cat nicebase|sed 's/%. \(A......\).*/\1/g'|sort|uniq` ; do echo $$i ; grep -h "%. $$i" eisBTfry* >>nicebaselist ; done