about the Index (long message)

[N. J. A. Sloane]

For those who are curious, the Index files are created
automatically when I do an update.  

The source file from which they are created is a single 5000-line flat file,
called  "locate_tab"  on my local machine.

I will put the first 500 lines here so you can see the format.

If anyone wants to send me some lines to add to this file that would be fine.

I don't have time right now to make any major
changes to the way the Index is run though.

Neil

Aa DIVIDER
0^n: A000007
a(a(n)) = 2n and similar sequences, <a NAME="aan">(start):</a>
a(a(n)) = 2n and similar sequences: (1) A000027 A002516 A002517 A002518 A003605 A007378 A007379 A054786 A054787 A054788 A054789 A054790
a(a(n)) = 2n and similar sequences: (2) A079000 A079253 A079905 A080588 A080589 A080591 A080596 A080637
a(a(n)) = 2n and similar sequences: see also: (1) A000201 A001462 A007479 A038752 A038755 A038756 A038757 A054048 A054049 A054791 A054792 A054793
a(a(n)) = 2n and similar sequences: see also: (2) A065804
a(n+1)=a(n)^2 + ..., <a NAME="AHSL">recurrences of the form (start):</a>
a(n+1)=a(n)^2 + ..., recurrences of the form, (1) A000058 A000289 A000324 A001042 A001056 A001146 A001510 A001543 A001566 A001696 A001699 A001999
a(n+1)=a(n)^2 + ..., recurrences of the form, (2) A002065 A003010 A003095 A003096 A004019 A028300 A051179
A(n, d), maximal size of binary code of length n and minimal distance d, <a NAME="And">sequences related to (start):</a>
A(n,3), maximal size of binary code of length n and minimal distance 3: A005864*
A(n,4), maximal size of binary code of length n and minimal distance 4: A005864*
A(n,5), maximal size of binary code of length n and minimal distance 5: A005865*
A(n,6), maximal size of binary code of length n and minimal distance 6: A005865*
A(n,7), maximal size of binary code of length n and minimal distance 7: A005866*
A(n,8), maximal size of binary code of length n and minimal distance 8: A005866*
A(n,d,w)  , maximal size of binary code of length n, constant weight w and minimal distance d, <a NAME="Andw">sequences related to (start):</a>
A(n,d,w) sequences (1): A001839 A001843 A004035 A004036 A004037 A004038 A004039 A004043 A004047 A004052 A004056 A004067
A(n,d,w) sequences (2): A005851 A005852 A005853 A005854 A005855 A005856 A005857 A005858 A005859 A005860 A005861 A005862
A(n,d,w) sequences (3): A005863
a/b + b/c + c/a = n: A072716
A2 lattice, <a NAME="A2">(also known as hexagonal or triangular lattice) sequences related to (start):</a>
A2 lattice, coordination sequence for: A008458*
A2 lattice, crystal ball sequence for: A003215*
A2 lattice, numbers represented by: A003136*
A2 lattice, polygons on: A036418*
A2 lattice, sublattices of: A003051*, A003050*, A054384*
A2 lattice, theta series of: A004016*, A035019*
A2 lattice, theta series of: see also A005881, A005882, A014202
A2 lattice, walks on: A001334*
A3 lattice: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Fa.html#fcc">f.c.c. lattice</a>
A3* lattice: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Ba.html#bcc">b.c.c. lattice</a>
A4 lattice, <a NAME="A4">sequences related to (start):</a>
A4 lattice, coordination sequence for: A008383*
A4 lattice, crystal ball sequence for: A008384*
A4 lattice, theta sequence for: A008444*
Ab DIVIDER
abelian numbers: A051532
absolute primes: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primes">primes, absolute</a>
abundance: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Ab.html#abundancy">abundancy</a>
abundancy , <a NAME="abundancy">sequences related to (start):</a>
abundancy: A033880*, A033879, A005579, A005347, A005580, A033881, A033882
abundancy: see also <a href="http://www.research.att.com/~njas/sequences/Sindx_De.html#deficiency">deficiency</a>
abundant numbers: A002093, A002182, A005101*, A006038
abundant numbers: see also A004394
acetylene: A000642, A005957
Ackermann function: A001695, A046859, A014221
acyclic digraphs, see <a href="http://www.research.att.com/~njas/sequences/Sindx_Di.html#digraphs">digraphs, acyclic</a>
add 1, multiply by 1, add 2, multiply by 2, etc.: A019463, A019460, A019462, A019461, A082448
add m then reverse digits: A007396, A003608, A007397, A007398, A007399
addition chains: A003064* A003065* A003313* A005766 A008057 A008928 A010787 A079300
additive bases , <a NAME="additive">sequences related to (start):</a>
additive bases: A004133, A004135, A004136
additive bases: see also <a href="http://www.research.att.com/~njas/sequences/Sindx_Go.html#Golomb">Golomb rulers</a>
Aho-Sloane paper: see entry for <a href="http://www.research.att.com/~njas/sequences/Sindx_Aa.html#AHSL">a(n+1)=a(n)^2 + ...</a>
Airey's converging factor: A001662
Aitken's array: A011971*
Al DIVIDER
alcohols: A000598 A000599 A000600 A002094 A005955 A005956
Alcuin's sequence: A005044*
algebras, Jordan: A001776
algebras: (1) A000929 A001330 A001331 A006448 A007154 A007156 A007157 A007158 A007159 A014610 A046001 A052249
algebras: (2) A052250 A052253
algebras; see also <a href="http://www.research.att.com/~njas/sequences/Sindx_Cl.html#cliff">Clifford group</a>, <a href="http://www.research.att.com/~njas/sequences/Sindx_Li.html#Lie">Lie algebras</a>, <a href="http://www.research.att.com/~njas/sequences/Sindx_V.html#VOA">vertex operator algebras</a>
algorithms: A005825 A005826 A005827 A006457 A006458 A006459 A006929 A030547 A032426 A049476 A055633
algorithms: see also <a href="http://www.research.att.com/~njas/sequences/Sindx_Eu.html#EucAlg">Euclidean algorithm</a>
aliquot parts: A001065* (sum of)
aliquot sequence (or trajectory) for n, length of: A098007*, A098008*, A003023, A044050*, A007906, A003062
aliquot trajectories for certain starting values: (1) A008885 A008886 A008887 A008888 A008889 A008890 A008891 A008892 A014360 A014361 A074907 A014362
aliquot trajectories for certain starting values: (2) A045477 A014363 A014364 A014365 A074906
alkanes: A000602*
alkyls: A000598 A000639 A000642 A000645 A000646 A000647 A000648 A000649 A000650 A005957 A010372 A022014 A036996
all-0's sequence: A000004*
all-1's sequence: A000012*
all-2's sequence: A007395*
all-3's sequence: A010701*
all-4's sequence: A010709*
all-5's sequence: A010716*
all-6's sequence: A010722*
all-7's sequence: A010727*
all-8's sequence: A010731*
all-9's sequence: A010734*
almost primes: (0) a k-almost prime has k prime factors, counted with multiplicity
almost primes: (1) A001358, A014612, A014613, A014614, A046306, A046308, A046310, A046312, A046314, A069272, A069273, A069274
almost primes: (2) A069275, A069276, A069277, A069278, A069279, A069280, A069281; table A078840.
almost-natural numbers: A007376
alphabetical order, numbers in: A000052*
alphabetical order, numbers in: see also A001058, A001061, A001062, A003588
alternating bit sets: A002487
alternating bit sum: A065359
alternating group A_m, degrees of irreducible representations of, for m = 5 through 13: A003860, A003861, A003862, A003863, A003864, A003865, A003866, A003867, A003868
alternating group A_n: A001710*
alternating permutations: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#perm">permutations, alternating</a>
alternating sign matrices: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Mat.html#ASM">matrices, alternating sign</a>
Am DIVIDER
amicable numbers, <a NAME="amicable">sequences related to (start):</a>
amicable numbers: A063990*, A063991 (unitary)
amicable pairs, augmented: A007992*, A015630*
amicable pairs, unitary: A002952*, A002953*
amicable pairs: A002025*, A002046*
ammonium: A000633
AND(x,y): A004198*
AND: see also: A003985 A005756 A006581 A007461 A033458 A046951 A050600 A050601 A050602 A051122 A053623
Andrews-Mills-Robbins-Rumsey numbers: A005130
animals, <a NAME="animals">sequences related to (start):</a>
animals, square: A000105
animals: (1) A001931 A005773 A005774 A005775 A006193 A006194 A006801 A006861 A007193 A007194 A007195 A007196
animals: (2) A007197 A007198 A007199 A010374 A011789 A011790 A011791 A011792 A033565 A036908 A038151 A038168
animals: (3) A038169 A038170 A038171 A038172 A038173 A038174 A038180 A038181 A038386 A039700 A039740 A039741
animals: (4) A039742 A053022 A055898 A055907 A055919
anti-divisors: A066272
antichains: A000372*, A007363*
antichains: see also (1) A003182 A006360 A006361 A006362 A007153 A007852 A007853 A014466 A032263 A051303 A051304 A051305
antichains: see also (2) A051306 A051307 A056932 A056933 A056934 A056935 A056936 A056937 A056939 A056940 A056941
antidiagonals, definition by example: A003987, A060736, A060734
antimagic squares: A050257
Ap DIVIDER
Apery numbers, <a NAME="Apery">sequences related to (start):</a>
Apery numbers: A002736*, A005258*, A005259*, A005429*, A005430*
Apery numbers: see also A006353, A006354
Apery's number zeta(3): A002117*, A013631*; see also A033165, A033166, A033167
Apocalyptic powers: A007356
Apollonian ball packings: A045506
Apollonian circle packings: A042944, A042945, A042946, A045673, A045864, A045963
approximate squaring: see under x*ceiling(x), iterating and x*floor(x), iterating
ApSimon mints problem: A007673
Ap\'{e}ry numbers: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Ap.html#Apery">Apery numbers</a>
Ar DIVIDER
arborescences: A003120
arc-cotangent reducible numbers: A002312
arccos(x): see Pi/2-arcsin(x), A055786 / A002595
arccosec(x): see arcsin(1/x), A055786 / A002595
arccosech(x): see arcsinh(1/x), A055786 / A002595
arccosh(x): A052468/A052469
arcos and arccos are both used in the database!
arcosh and arccosh are both used in the database!
arcsec(x): see Pi/2-arcsin(1/x), A055786 / A002595
arcsech(x): see arccosh(1/x), A052468 / A052469
arcsin(x): A055786/A002595, A006228
arcsinh(x): A055786/A002595
arctangent numbers, triangle of: A008309*
areas: A005386
ARIBAS: A062916
arithmetic means: A007340
arithmetic numbers: A003601*, A090944
arithmetic progressions: A003407, A005115, A005836, A005837, A005838, A005839
Armstrong numbers, <a NAME="Armstrong">sequences related to (start):</a>
Armstrong numbers: A005188*
Armstrong numbers: in other bases: A010343, A010344, A010345, A010346, A010347, A010348, A010349, A010350, A010351, A010352, A010353, A010354
Armstrong numbers: see also A014576
Aronson's sequence : A005224*
Aronson's sequence, generalized: A079000
Aronson's sequence, generalized: see also <a href="http://www.research.att.com/~njas/sequences/Sindx_Aa.html#aan">sequences of the a(a(n)) = 2n family</a>
Aronson's sequence, numerical analogues of: ( 1) A000201 A003151 A003605 A004956 A005224 A007378 A010906 A014132 A026351 A045412 A061891 A064437
Aronson's sequence, numerical analogues of: ( 2) A073074 A079000* A079250 A079251 A079252 A079253 A079254 A079255 A079256 A079257 A079258 A079259
Aronson's sequence, numerical analogues of: ( 3) A079313 A079325 A079351 A079358 A079905 A079946 A079948 A080029 A080030 A080031 A080032 A080033
Aronson's sequence, numerical analogues of: ( 4) A080034 A080036 A080037 A080081 A080199 A080353 A080455 A080456 A080457 A080458 A080460 A080574
Aronson's sequence, numerical analogues of: ( 5) A080578 A080579 A080580 A080588 A080589 A080590 A080591 A080600 A080633 A080637 A080639 A080640
Aronson's sequence, numerical analogues of: ( 6) A080641 A080644 A080645 A080646 A080652 A080653 A080667 A080707 A080708 A080710 A080711 A080712
Aronson's sequence, numerical analogues of: ( 7) A080714 A080720 A080722 A080723 A080724 A080725 A080726 A080727 A080728 A080731 A080745 A080746
Aronson's sequence, numerical analogues of: ( 8) A080752 A080753 A080754 A080759 A080760 A080780 A080900 A080901 A080903 A080904 A080939 A080949
Aronson's sequence, numerical analogues of: ( 9) A081023 A081024 A081260 A081746 A091387 A091388 A091389 A091390 A091391
arrays, indexing: see <a href="http://www.research.att.com/~njas/sequences/a073189.txt">a073189.txt</a>
arrays, sequences used for indexing: (1) A000194 A002024 A002260 A002262 A003056 A003057 A003059 A004736 A025581 A048760 A053186 A055086
arrays, sequences used for indexing: (2) A055087 A071797 A073188 A073189
arrays: A003169, A007073, A007074, A007072
artiads: A001583*
Artin's conjecture  or constant, <a NAME="Artin">sequences related to (start):</a>
Artin's conjecture : A001122
Artin's conjecture, Artin's constants: A005596* A048296* A065414 A065417 A066517
Artin's conjecture: see also <a href="http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primes_root">primes by primitive root</a>
association schemes: A057495*, A057498 (noncommutative), A057499 (primitive)
asymmetric channel, codes for: A010101
asymmetric sequences: A002842
asymptotic expansions:  A001163 A001164 A002073 A002074 A002304 A002305 A002514 A006572 A006953
atomic species: A005226, A005227, A007650
atomic weights: A007656*
audioactive decay: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Sa.html#swys">"say what you see"</a>
autobiographical numbers: A104784, but see also self-describing numbers
automata, see <a href="http://www.research.att.com/~njas/sequences/Sindx_Ce.html#cell">cellular automata</a>
automorphic numbers , <a NAME="automorphic">sequences related to (start):</a>
automorphic numbers: (1) A003226 A007185 A016090 A018247 A018248 A033819 A074194 A074250 A074321 A074330 A074332
automorphic numbers: (2) A030984 A030985 A030986 A030987 A030988 A030989 A030990 A030991 A030992 A030993 A030994
automorphic numbers: (3) A030995 A035383 A046883 A046884 A082576
automorphic numbers: see also A045537, A075154
A_2 lattice: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Aa.html#A2">A2 lattice</a>
A_3 lattice: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Fa.html#fcc">f.c.c. lattice</a>
A_4 lattice: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Aa.html#A4">A4 lattice</a>
A_n lattice: coordination sequence for: see A005901.
A_n sequence, primes in: A111157
Ba DIVIDER
B-trees: A014535*, A037026, A058521, A058518, A058519, A058520
b.c.c. lattice , <a NAME="bcc">sequences related to (start):</a>
b.c.c. lattice, <a href="http://www.research.att.com/~njas/lattices/Ds3.html">home page for</a>
b.c.c. lattice, animals on:  A007195 A007196 A007197 A038170 A038171 A038180 A038181 A038386
b.c.c. lattice, coordination sequence for: A005897*
b.c.c. lattice, partition function: A001406
b.c.c. lattice, polygons on: A001667
b.c.c. lattice, series expansions for: (1) A002167 A002168 A002914 A002917 A002925 A003194 A003206 A003210 A003492 A003497 A007218 A006805
b.c.c. lattice, series expansions for: (2) A006811 A006838 A007218 A010559 A010560 A010564 A047711
b.c.c. lattice, theta series of: A004013* A004014* A004024 A004025 A005869 A008664 A008665
b.c.c. lattice, walks on: A001666, A001667, A002903
Baby Monster simple group: A001378*
backgammon: A055100
Baker-Campbell-Hausdorff expansion: A005489
balanced numbers: A020492
Balancing weights: A002838
ballot numbers , <a NAME="ballot">sequences related to (start):</a>
ballot numbers: A003121*
ballot numbers: see also A002026, A006123, A007054, A007272, A034928, A034929
balls into boxes: (1) A000110 A001700 A001861 A005337 A005338 A005339 A005340 A007318 A019575 A019576 A019577 A019578
balls into boxes: (2) A019579 A019580 A019581 A027710
balls on the lawn: see tennis ball problem
Barker sequences (or Barker codes): A011758, A011759, A091704
Barnes-Wall lattices, <a NAME="BW">sequences related to (start):</a>
Barnes-Wall lattices, groups of: A014115*, A014116*
Barnes-Wall lattices, in 2^2 dim., theta series of: A004011
Barnes-Wall lattices, in 2^3 dim., theta series of: A004009
Barnes-Wall lattices, in 2^4 dim., theta series of: A008409
Barnes-Wall lattices, in 2^5 dim., theta series of: A004670
Barnes-Wall lattices, in 2^6 dim., theta series of: A103936
Barnes-Wall lattices, in 2^7 dim., theta series of: A100004
Barnes-Wall lattices, kissing numbers of: A006088*
Barnes-Wall lattices, odd: A014711*
Barnes-Wall lattices, see also A035596
Barnes-Wall lattices, vectors of twice minimum: A110972, A110973
Barnes-Wall lattices: see also <a href="http://www.research.att.com/~njas/sequences/Sindx_Cl.html#cliff">Clifford groups</a>
barriers for omega(n): A005236
barycentric subdivisions: A002050, A005461, A005462, A005463, A005464
base -2: A939724*, A005351*, A005352
base, factorial, A007623
base, fractional, definition: A024661*
base, fractional: defined in A024630
baseball: see Ruth-Aaron numbers, Maris-McGwire numbers
bases, various (1):: A003137, A005358, A007095, A007094, A005377, A007093, A007092, A007091, A005357, A007090
bases, various (2):: A007608, A001357, A007633, A007089, A006941, A005352, A006288, A007632, A005356, A003166
bases, various (3):: A002442, A002441, A002440, A005936, A005351, A005938, A005939, A007088, A006993, A000468, A005937, A005935, A007535, A001567
Batcher parallel sort: A006282
Baxter permutations: A001181*, A001183*, A001185*
bcc lattice: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Ba.html#bcc">b.c.c. lattice</a>
Be DIVIDER
Beans-Don't-Talk: A005694, A005695, A005696, A005697, A005698
Beanstalk: A005692, A005693
Beatty sequences   <a NAME="Beatty">(start):</a>
Beatty sequences  : for a constant c, the two Beatty sequences are the main sequence floor(n*c) and the complementary sequence floor(n*c') where c' = c/(c-1)).
Beatty sequences for: (n+1/2)/2 (A038707), (n+1/2)/4 (A038709), Feigenbaum's constant (A038123), Brun's constant (A038124)
Beatty sequences for: (sqrt(5)+5)/2 (A003231), (1 + sqrt 3)/2 (A003511), sqrt 3 + 2 (A003512), (3+Sqrt[3])/2 (A054406)
Beatty sequences for: 1+1/Pi (A059531), 1+Pi (A059532), 1+Catalan's constant (A059533), 1+1/Catalan's constant (A059534)
Beatty sequences for: 1+gamma A001620 (A059555), 1+1/gamma (A059556), 1+gamma^2, (A059557), 1+1/gamma^2 (A059558), 1-ln(1/gamma), (A059559), 1-1/ln(1/gamma) (A059560)
Beatty sequences for: 3/4, 2/5, 3/5, 2/7, 3/7, 4/7, 5/7, 3/8, 5/8, 5/13, 8/13, 8/21, 13/21, 7/19, 11/30 (A057353-A057367)
Beatty sequences for: 3^(1/3) (A059539), 3^(1/3)/(3^(1/3)-1) (A059540), 1+ln(2) (A059541), 1+1/ln(2) (A059542), ln(3) (A059543), ln(3)/(ln(3)-1) (A059544)
Beatty sequences for: e (A022843), e/(e-1) (A054385), 1/(e-2) (A000062), 1/e (A032634), e-1 (A000210), e+1 (A000572), (e+1)/e (A006594), e^(1/e) (A037087)
Beatty sequences for: e^gamma (A059565), e^gamma/(e^gamma-1) (A059566), 1-ln(ln(2)) (A059567), 1-1/ln(ln(2)) (A059568)
Beatty sequences for: e^pi (A038152), pi^e (A038153), 2^sqrt(2) (A038127), Euler's gamma (A038128), 2^(1/3) (A038129)
Beatty sequences for: Gamma(1/3) (A059551), Gamma(1/3)/(Gamma(1/3)-1) (A059552), Gamma(2/3) (A059553), Gamma(2/3)/(Gamma(2/3)-1) (A059554)
Beatty sequences for: ln(10) (A059545), ln(10)/(ln(10)-1) (A059546), 1+1/ln(3) (A059547), 1+ln(3) (A059548), 1+1/ln(10) (A059549), 1+ln(10) (A059550)
Beatty sequences for: ln(Pi) (A059561), ln(Pi)/(ln(Pi)-1) (A059562), e+1/e (A059563), (e^2+1)/(e^2-e+1) (A059564)
Beatty sequences for: Pi (A022844), Pi/(Pi-1) (A054386), 1/Pi (A032615), pi^2 (A037085), sqrt(pi) (A037086), 2*pi (A038130), sqrt(2 pi)  (A038126)
Beatty sequences for: Pi^2/6, or zeta(2) (A059535), zeta(2)/(zeta(2)-1) (A059536), zeta(3) (A059537), zeta(3)/(zeta(3)-1) (A059538)
Beatty sequences for: sqrt(2) (A001951), 2 + sqrt(2) (A001952), 1 + 1/sqrt(11) (A001955), 1 + sqrt(11) (A001956)
Beatty sequences for: sqrt(3) (A022838), sqrt(5) (A022839), sqrt(6) (A022840), sqrt(7) (A022841), sqrt(8) (A022842)
Beatty sequences for: sqrt(5) - 1 (A001961), sqrt(5) + 3 (A001962), 1+sqrt(2) (A003151), 1/(2-sqrt(2)) (A003152)
Beatty sequences for: tau (A000201), tau^2 (A001950), tau^3 (A004976), tau^(4+n) (n=0..16) (A004919+n)
Beatty sequences: references about: see especially A000201
Beatty sequences: see also (1) A014245 A014246 A022803 A022804 A022805 A022806 A022879 A022880 A023541 A023542 A045671 A045672
Beatty sequences: see also (2) A045681 A045682 A045749 A045750 A045774 A045775
Beethoven: A001491, A054245
beginning with t: A006092, A005224
Bell numbers: A000110*
Bell numbers: see also A007311
bell ringing , <a NAME="bell_ringing">sequences related to (start)</a>
bell ringing: (1) A090277 A090278 A090279 A090280 A090281 A090282 A090283 A090284
bell ringing: (2) A057112 A060112 A060135
Bell's formula: A002575, A002576
bending: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Fo.html#fold">folding</a>
Benford numbers: A004002*
Benny, Jack: A056064
benzene: A000639
Berlekamp's switching game: A005311*
Bernoulli numbers  , <a NAME="Bernoulli">sequences related to (start):</a>
Bernoulli numbers  B_n: A027641**/A027642*. A027641 has all the references, links and formulae.
Bernoulli numbers  B_{2n}: A000367*/A002445*, but see especially A027641
Bernoulli numbers (n+1)B_n: A050925/A050932, A002427/A006955
Bernoulli numbers, generalized: A006568, A006569, A002678, A002679
Bernoulli numbers, higher order: A001904, A001905
Bernoulli numbers, numerators and their factorizations: (1) A000367 = numerators, A000928 = irregular primes, A001067 A001896 A002427 A002431 A002443 A002657 A007703 A017329 A027641 A027643
Bernoulli numbers, numerators and their factorizations: (2) A027645 A027647 A029762 A029764 A033470 A033474 A035078 A035112 A043295 A043303 A046988 A050925
Bernoulli numbers, numerators and their factorizations: (3) A053382 A060054 A067778 A068206 A068399 A068528 A069040 A069044 A070192 A070193 A071020 A071772
Bernoulli numbers, numerators and their factorizations: (4) A073276 A075178 A076547 A076549 A079294 = number of prime factors, A083687 A084217 A085092 A085737 A089170 A089644 A089655
Bernoulli numbers, numerators and their factorizations: (5) A090177 A090179 A090495 A090496 A090629 A090789 A090790 A090791 A090793 A090798 A090800 A090817
Bernoulli numbers, numerators and their factorizations: (6) A090818 A090823 A090825 A090865 A090943 = squareful numerators, A090947 = largest prime factor, A091216 A091888 A092132 A092133 A092194 A092195
Bernoulli numbers, numerators and their factorizations: (7) A092221 A092222 A092223 A092224 A092225 A092226 A092227 A092228 A092229 A092230 A092231 A092291
Bernoulli numbers, numerators and their factorizations: (8) A090997 A090987
Bernoulli numbers, poly-Bernouli numbers: A027643 A027644 A027645 A027646 A027647 A027648 A027649 A027650 A027651
Bernoulli numbers, see also (1): A000146 A000182 A000928 A001469 A001896 A001947 A002105 A002208 A002316 A002431 A002443 A002444
Bernoulli numbers, see also (2): A002657 A002790 A002882 A003245 A003264 A003272 A003326 A003414 A003457 A004193 A006863 A006953
Bernoulli numbers, see also (3): A006954 A014509 A020527 A020528 A020529 A029762 A029763 A029764 A029765 A030076 A033469 A033470
Bernoulli numbers, see also (4): A033471 A033473 A033474 A033475 A035077 A035078 A035112 A045979 A046094 A046968 A047680 A047681
Bernoulli numbers, see also (5): A047682 A047683 A047872 A051222 A051225 A051226 A051227 A051228 A051229 A051230
Bernoulli numbers, see also (6): A027762
Bernoulli numbers, triangles that generate: A051714/A051715, A085737/A085738
Bernoulli polynomials, coefficients of: A053382*/A053383*, A048998*, A048999*
Bernoulli polynomials, see also A001898 A002558 A020527 A020528 A020529 A020543 A020544 A020545 A020546
Bernstein squares: A097871
Berstel sequence: A007420*
Bertrand's Postulate: A035250*, A036378, A006992, A051501
Bessel function or Bessel polynomial , <a NAME="Bessel">sequences related to (start):</a>
Bessel function or Bessel polynomial: (1) A000134 A000155 A000167 A000175 A000249 A000275 A000331 A001880
Bessel function or Bessel polynomial: (2) A001881 A002190 A002506 A006040 A006041 A014401 A039699 A046960 A046961 A046962 A046963
Bessel function or Bessel polynomial: (3) A051148 A051149 
Bessel functions:  J_0: A002454, J_1: A002474, J_2: A002506, J_3: A014401, J_4: A061403, J_5: A061404, J_6: A061405, J_7: A061407, J_9: A061440 J_10: A061441
Bessel numbers: A006789, A111924, A100861
Bessel polynomial, coefficients of: A001497, A001498
Bessel polynomial, defined: A001515, A001497, A001498
Bessel polynomial, values of: (1) A001515, A001517, A001518, A065919, A001514, A065920, A065921, A065922, A006199, A065707, A000806, A002119
Bessel polynomial, values of: (2) A065923, A001516, A065944, A065945, A065946, A065947, A065948, A065949, A065950, A065951
Bessel triangle: A001497*, A000369,  A001498, A011801, A013988, A004747, A049403, A065931, A065943
betrothed numbers: A003502*, A003503*, A005276*
Bi DIVIDER
bicoverings: A002718, A002719
bigomega(n), number of primes dividing n (counted with repetition): A001222
binary codes, maximal size of constant weight, see <a href="http://www.research.att.com/~njas/sequences/Sindx_Aa.html#Andw">A(n,d,w)</a>
binary codes, maximal size of, see <a href="http://www.research.att.com/~njas/sequences/Sindx_Aa.html#And">A(n, d)</a>
binary codes: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Coa.html#codes_binary_linear">codes, binary</a>
binary digits: see binary expansion
binary entropy: A003314
binary expansion of n , <a NAME="binary">sequences related to (start):</a>
binary expansion of n: A000120*, A000788*, A000069*, A001969*, A023416*, A059015*, A007088*, A070939*
binary expansion of n: see also (1) A005536, A003159, A006995, A006364, A054868, A070940, A070941, A070943, A001511, A029837, A037800
binary expansion of n: see also (2) A014081, A014082
binary matrices: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Mat.html#binmat">matrices, binary</a>
binary order of n: A029837, A070939
binary partitions: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Par.html#part">partitions, binary</a>
binary quadratic forms: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Qua.html#quadform">quadratic forms</a>, binary
Binary sequences:: A006840
binary strings of length n: A007931*
binary strings, see also: A007039, A007040, A005598
binary vectors, grandchildren of: A057606, A057607, A000124
Binary vectors:: A005253, A003440
binary weight of n: A000120*
binomial coefficient, <a NAME="binomial">sequences related to (start):</a>
binomial coefficients, A000012* = C(n,0), A000027* = C(n,1), A000217* = C(n,2), A000292* = C(n,3), etc.
binomial coefficients, central: A000984*, A001405*, A001700
Binomial coefficients, lcm of:: A002944
Binomial coefficients, occurrences of n as:: A003016
binomial coefficients, triangle of: A007318*
binomial coefficients: (1):: A005733, A005735, A005809, A001791, A005810, A000332, A002054, A000389, A002694, A003516
binomial coefficients: (2):: A000580, A002696, A000581, A000582, A001287, A001288
binomial coefficients: see also trinomial coefficients, quadrinomial coefficients
Binomial coefficients: sums:: A001527, A003161, A003162
Binomial moments:: A000910
binomial transform, <a NAME="binomial_transform">sequences related to (start):</a>
binomial transform: see <a href="http://www.research.att.com/~njas/sequences/transforms.txt">Transforms</a> file
Binomial transforms:: A007442, A000371, A007476, A007443, A007317, A005331, A007405, A007472, A004211, A005572, A005494, A004212, A005021, A004213, A005011, A005327, A005014
binomial(n,k): binomial coefficient n-choose-k (see A007318)
bipartite (1):: A007083, A007029, A000291, A006823, A006612, A002774, A007085, A005142, A000412, A004100
bipartite (2):: A001832, A005335, A005336, A007084, A002762, A002766, A002763, A006824, A006825, A007028
bipartite (3):: A002767, A000465, A002768, A002764, A000491, A002765, A002755, A002756, A002757, A002758, A002759
bipartite graphs: see graphs, bipartite
biprimes: A001358
birthday paradox: A014088 A033810 A050255 A050256 A051008 A064619
bisections: see also dissections
Bisections:: A001519, A002478, A001906, A002878, A002287, A002286
Bishops problem:: A005633, A005631, A005635, A002465*, A005634, A005632
bits: see binary expansion
Bl DIVIDER
blobs: A003168 A007161 A007166 A048173
blocks: see also LEGO blocks
blocks: see also under <a href="http://www.research.att.com/~njas/sequences/Sindx_Par.html#part">partitions</a>
blocks: see graphs, nonseparable
Bo DIVIDER
Board of Directors Problem: A005254, A037354
Bode's law: A003461*, A061654
body-centered cubic lattice: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Ba.html#bcc">b.c.c. lattice</a>
Bohr radius: A003671*
Bokmal: A014656
Bond percolation:: A006727, A006728, A006730, A006738, A006729, A006735, A006736, A006737
Boolean functions, <a NAME="Boolean">sequences related to (start):</a>
Boolean functions, balanced: A000721
Boolean functions, cascade-realizable: A005608, A005609, A005610, A005611, A005613, A005619, A005749
Boolean functions, Dedekind's problem: see Boolean functions, monotone (Dedekind's problem)
Boolean functions, fanout-free: A005737, A005736, A005742, A005738, A005740, A005612, A005615, A005617, A005743, A005741
Boolean functions, inequivalent, under action of various groups (1): A000133, A000214, A000231, A000585, A000614, A001289, A003180, A008842, A011782, A028401, A028402, A028403
Boolean functions, inequivalent, under action of various groups (2): A028404, A028405, A028406, A028407, A028409, A028410, A028411, A049461, A051460, A051502, A053040, A057132
Boolean functions, invertible: A001038, A000656, A000653, A000722, A000654, A000725, A000724, A000723, A001537, A000652
Boolean functions, irreducible: A000616*
Boolean functions, minimal numbers of elements needed to realize any: A056287*, A057241*, A058759*
Boolean functions, monotone (Dedekind's problem): A000372*, A003182*, A007153*, A001206*, A014466*
Boolean functions, monotone (Dedekind's problem): see also A016269, A047707, A051112, A051113, A051114, A051115, A051116, A051117, A051118
Boolean functions, monotone (Dedekind's problem): see also Dedekind's problem
Boolean functions, nondegenerate: A000371*, A000618, A003181, A001528
Boolean functions, see also (1): A000157, A000370, A000612, A000613, A001087, A005530, A005581, A005744, A005756, A018926, A036240, A037267
Boolean functions, see also (2): A037843, A051185, A051355, A051360, A051361, A051368, A051375, A051376, A051381, A056778
Boolean functions, see also <a href="http://www.research.att.com/~njas/sequences/Sindx_Sw.html#switching">switching networks</a>
Boolean functions, see also canalizing functions
Boolean functions, see also threshold functions
Boolean functions, self-complementary: A000610*, A001320*, A053037
Boolean functions, self-dual monotone: A001206*
Boolean functions, self-dual: A001531*, A006688*, A002080, A008840, A008841
Boolean functions, triangle of numbers of: A039754, A051486*, A053874*, A052265*, A054724*, A022619*, A059090
Boolean functions, unate: A003183
Boolean lattices: A005493
boson strings: A005290 A005291 A005292 A005293 A005294 A005307 A005308
bouquets: A005431
boustrophedon transform, <a NAME="boustrophedon">sequences related to (start):</a>
boustrophedon transform, definition see <a href="http://www.research.att.com/~njas/doc/bous.txt">Millar-Sloane-Young paper</a>
boustrophedon transform, in Maple, see <a href="http://www.research.att.com/~njas/sequences/transforms.txt">Transforms</a> file
boustrophedon transform, of various sequences: (0) A000111*, A000182*, A000364*, A000667*
boustrophedon transform, of various sequences: (1) A000660 A000674 A000687 A000697 A000718 A000732 A000733 A000734 A000736 A000737 A000738
boustrophedon transform, of various sequences: (2) A000744 A000745 A000746 A000747 A000751 A000752 A000753 A000754 A000756 A000764 A029885
boustrophedon transform, variations on: (1) A059216, A058217, A059219, A059220, A059502, A059503, A059505, A059506, A059507, A059508, A059509, A059226
boustrophedon transform, variations on: (2) A059227, A059228, A059229, A059234, A059235, A058237
boustrophedon transform, variations on: (3) A059510 - A059512, A027994
boustrophedon transform: see also A000661
bowling: A060853
Br DIVIDER
bracelets , <a NAME="bracelets">sequences related to (start):</a>
bracelets , A000029*, A005232, A005513-A005516, A007123, A032279-A032288, A073020, A078925
bracelets, 3-colored, A005654, A005656, A027671*, A032240, A032294
bracelets, 4-colored, A032241, A032275*, A032295
bracelets, 5-colored, A032242, A032276*, A032296
bracelets, aperiodic, A001371*, A032294-A032296, A045628, A045633
bracelets, asymmetric, A032239*, A032240-A032242
bracelets, balanced, A005648*, A006079, A006840, A045628, A045633
bracelets, complements are equivalent, A000011*, A006080, A006840, A045633, A053656, A066313-A066316
bracelets, identity, see bracelets, asymmetric
bracelets, triangle, A052307*, A052308, A052309, A052310
bracelets: see also <a href="http://www.research.att.com/~njas/sequences/Sindx_Lu.html#Lyndon">Lyndon words</a>, <a href="http://www.research.att.com/~njas/sequences/Sindx_Ne.html#necklaces">necklaces</a>
bracelets: see also A005595, A007148, A027670, A054499
bracket function: A000748, A000749, A000750, A001659 , A006090
brackets, ways to arrange: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Par.html#parens">parentheses, ways to arrange</a>
braids: A054761*, A000071, A054480, A007988, A007990, A007991, A007993, A007994, A007995
Braille: A079399, A072283
Bravais lattices: A004030*
bricks , <a NAME="bricks">(start):</a>
bricks: A000472 A003697 A006291 A006292 A006293 A031173 A031174 A031175
bridge hands, sorting: A065603
Brun's constant: A065421, A005597, A038124
Buffon's needle: A060294*
building numbers from other numbers and the operations of addition, subtraction, etc: see under <a href="http://www.research.att.com/~njas/sequences/Sindx_Fo.html#4x4">four 4's problem</a>
bull (in graph theory): see A079577
Burnside's problem in group theory: A051576, A079682, A079683
Busy Beaver problem , <a NAME="beaver">(start):</a>
Busy Beaver problem: A028444*, A004147*, A060843*, A052200
Busy Beaver problem: see also Turing machines
B_2 sequences , <a NAME="B_2">(start):</a>
B_2 sequences: A005282, A010672, A011185, A025582
B_n lattice: coordination sequence for: see A022145.
Ca DIVIDER
C(n,2): A000217*
C(n,3): A000292*
C(n,4): A000332*
C(n,k): binomial coefficient n-choose-k (see A007318)
cacti , <a NAME="cacti">sequences related to (start):</a>
cacti, 2-ary: A054357*, A054358
cacti, 3-ary: A052393*, A054422
cacti, 4-ary: A052394*, A052395
cacti, 5-ary: A054363*, A054364
cacti, 6-ary: A054366*, A054367
cacti, 7-ary: A054369*, A054370
cacti, plane, 3-gonal: A054423
cacti, plane, 4-gonal: A054362
cacti, plane, 5-gonal: A054365
cacti, plane, 6-gonal: A054368
cacti, plane, 7-gonal: A054371
cacti, polygonal: A035082*, A035088*
cacti, rooted, polygonal: A035085*, A035086, A035087*
cacti, rooted, triangular: A002067, A003080*, A032035, A034940*, A091481, A091486, A091488
cacti, rooted, with bridges: A000237*, A035351*, A035352, A035353, A035357
cacti, triangular: A003081*, A034941*, A091485, A091487, A091489
cacti, with bridges: A000083* (unlabeled), A000314* (labeled), A035356
cage graphs: A052453, A052454
Cahen's constant: A006279, A006280, A006281
cake numbers: A000125*
calculator display: A006942* A010371* A018846 A018847 A018849 A038136 A053701 A063720
Cald's sequence: A006509*
calendar, <a NAME="calendar">sequences related to (start):</a>
calendar, dates of days in: A008684*
calendar, days in year: A011763*
calendar, days per century: A011770, A011771
calendar, lengths of months: A008685*
calendar: see also A001356, A031139, A051121
campanology: see <a href="http://www.research.att.com/~njas/sequences/Sindx_Be.html#bell_ringing">bell ringing</a>
canalizing Boolean functions: A102449, A109460, A109461, A109462
cannonball problem: see A001032
Cantor set: A005823
Cantor's sigma function: A055068
card arranging: A006063
card arranging: see also <a href="http://www.research.att.com/~njas/sequences/Sindx_So.html#sorting">sorting</a>
card games: see also <a href="http://www.research.att.com/~njas/sequences/Sindx_Poi.html#poker">poker</a>
card games: see also patience
card matching, <a NAME="cardmatch">sequences related to (start):</a>
card matching: (1) A000279 A000316 A000459 A000489 A000535 A059056 A059057 A059058 A059059 A059060 A059061 A059062
card matching: (2) A059063 A059064 A059065 A059066 A059067 A059068 A059069 A059070 A059071 A059072 A059073 A059074
card sorting: see <a href="http://www.research.att.com/~njas/sequences/Sindx_So.html#sorting">sorting</a>
Carmichael numbers , <a NAME="Carmichael">(start):</a>
Carmichael numbers: A002997*
Carmichael numbers: see also (1) A002322 A006931 A006972 A029553 A029554 A029555 A029556 A029557 A029558 A029559 A029560 A029561
Carmichael numbers: see also (2) A029562 A029563 A029564 A029565 A029566 A029567 A029568 A029569 A029570 A029590 A029591 A033502