[seqfan] Re: A064736, A217579 and A302350

[Antti Karttunen]

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> Message: 20
> Date: Thu, 12 Apr 2018 06:20:16 +0200 (CEST)
> From: michel.marcus at free.fr
> To: "seqfan " <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: A064736, A217579 and A302350
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> Hi all,
>
>
> Thanks for your answers.
> But my question was more like how do I find the sequences that have this
> property within the 302000+ OEIS sequences.
> If I search for link:""Index entries for sequences that are permutations
> of the natural numbers" I get 176 pages with 10 sequences each.
> I won't go to each sequence and copy the data section or save the source
> bfile with my browser.
>
>
> I would like to find the magical https//oeis.search/ query params that
> would return to me the list of all permutations sequences or the data for
> all of them in a single shot.
> Do we have this?
>
>
No as far as I know. But we have stripped.gz
So, adding a couple of extraneous routines to my OEIS Djinn script, I first
prepared from stripped data a file that contains only those Anums + terms
where the terms are injective (no repeated terms), and where the terms are
not monotonic (at least one negative value among their first differences).
Then, in second pass (this could be made in a single pass also, of course),
I search for cases for which after the first term, either each term divides
the previous, or vice versa:

        prevterm = 1
        satisfies_the_condition = 1

        for term in terms[1:]:
          if((0==term) or ((term % prevterm) and (prevterm % term))):
            satisfies_the_condition = 0
            break
          prevterm = term


        if(satisfies_the_condition):
          outfp.write(anum + " " + name_used)
          outfp.write("\n")
          suspected_cases += 1


I got the following 50 results (incidentally, your A217579 is not listed
there, and neither it should, as it begins 1, 4, 9, 8, 25, ... Or did I
understood wrongly what you were searching for?= But A064736, A302350 and
also A207901 that Peter Munn mentioned are included. It's up to you to
check which of the other ones are actually permutations of natural numbers:

A008336 a(n+1) = a(n)/n if n|a(n) else a(n)*n, a(1) = 1.
A009117 E.g.f.: 1/2 + exp(-4*x)/2.
A055634 2-adic factorial function.
A064736 a(1)=1, a(2)=2; for n>0, a(2*n+2) = smallest number missing
from {a(1), ... ,a(2*n)}, and a(2*n+1) = a(2*n)*a(2*n+2).
A065422 If n|a(n) then a(n+1) = a(n)/(highest power of n that divides
a(n)), otherwise a(n+1) = n*a(n); a(0) = 1.
A073925 Powers of 2 rearranged such that every partial sum (n>1) is composite.
A084039 a(1) = 1 and then distinct numbers such that the product of
two successive terms + 1 as well as the ratio of the larger to the
smaller of two successive terms + 1 is a prime.
A084244 a(0)=1, a(1)=5, a(n) = -3*a(n-1), n>1.
A084337 Rearrangement of natural numbers so that the successive ratios
( of the larger to the smaller term) are all distinct integers.
a(m)/a(m-1)= a(k)/a(k-1) iff m = k ( assuming a(m) > a(m-1) otherwise
the ratio a(m-1)/a(m) is to be considered). Priority is given to
smallest number not included earlier than to the successive ratio that
has not occurred earlier.
A085542 Determinant of the n X n matrix M_(i,j)=i/gcd(i,j)=lcm(i,j)/j.
A086482 Beginning with 1, the smallest number not included earlier
such that the n-th partial product is an n-th power; or the geometric
mean of the first n terms is an integer.
A089337 a(1) = 1; for n>1, a(n) is the smallest, either a divisor or a
multiple in that priority (order), of a(n-1) such that it is a
distinct palindrome not included earlier.
A094014 Expansion of (1-2x)/(1-8x^2).
A094299 a(0) = 1; for n>0, if gcd(a(n-1),n) = 1 then a(n) = n*a(n-1)
else a(n) = least integer multiple of a(n-1)/n.
A104537 Expansion of g.f.: (1+x)/(1+2*x+4x^2).
A111678 a(n+1) = least palindrome not already used that is either a
divisor or multiple of a(n) such that the ratios a(n+1)/a(n) are all
distinct.
A113552 Beginning with 1, least divisor of the previous term not
included earlier, otherwise the least multiple of the previous term
having at least one prime divisor coprime to it and not included
earlier.
A116570 a(2*n) = prime(n+1) * prime(n+2), a(2*n-1) = prime(n+1).
A117575 Expansion of (1-x^3)/((1-x)*(1+2*x^2)).
A119862 Smallest number not yet used that is either a divisor or
multiple of both n and a(n-1).
A120617 Hankel transform of g.f. 1/sqrt(1+4x^2).
A122803 Powers of -2.
A123344 Expansion of (1+3*x)/(1+2*x).
A135520 a(n) = 4*a(n-2).
A137206 First differences of A074323.
A137717 Hankel transform of A106191.
A138380 First differences of A138377.
A138382 First differences of A138380. Second differences of A138377.
A141125 Hankel transform of a transform of Fibonacci numbers.
A141413 Inverse binomial transform of A140962.
A152166 a(2*n)=2^n ; a(2*n+1)=-(2^(n+1)).
A155734 Binomial transform of A154879.
A157782 Denominator of Bernoulli(n, -1/2).
A157823 a(n) = A156591(n) + A156591(n+1).
A162852 a(n) = 3*a(n-2) for n > 2; a(1) = 3, a(2) = -1.
A163864 a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 6.
A164111 Expansion of (1-x)/(1+4*x^2).
A164703 a(n) = 8*a(n-2) for n > 2; a(1) = 1, a(2) = 16.
A166027 a(n) = 6*a(n-2) for n > 2; a(1) = 4, a(2) = 1.
A166450 a(n) = 3*a(n-2) for n > 2; a(1) = 1, a(2) = 6.
A171559 Powers of 2 (cf. A000079) with 1 replaced by 3.
A176414 Expansion of (7+8*x)/(1+2*x).
A207901 Let S_k denote the first 2^k terms of this sequence and let
b_k be the smallest positive integer that is not in S_k, also let R_k
equal S_k read in reverse order; then the numbers b_k*R_k are the next
2^k terms.
A248769 Greatest 5th-power-free divisor of n!.
A256096 Expansion of (4+3*x)/(1+3*x).
A274941 Trajectory of 2 under the map x -> A274940(x).
A281978 Lexicographically earliest sequence of distinct terms such
that, for any n>0, a(2n) is divisible by a(2n-1) and by a(2n+1).
A282291 Lexicographically earliest sequence of distinct terms such
that every pair of consecutive terms contains a term that is an
unitary divisor of the other term.
A284003 a(n) = A007913(A283477(n)).
A302350 Instance of a permutation of the positive integers such that
lcm(a(n), a(n+1)) <= c*n*log(n)^2.


So, if we had a subcategory for these kind of permutations, how it should
be called? "Multiple-or-divisor permutations" ?


Best regards,

Antti



>
> Best regards.
> Michel
>
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