A107357 -id:A107357 - cp's OEIS frontend

A037181 Incorrect version of A107357.

1, 2, 1, 0, 2, 3, 0, 6, 8, 4, 63, 1, 316, 42, 16, 2048, 7652, 13781, 8, 24000, 11977, 458561, 152116956851941670912, 1054535, 53, 26, 27, 59, 4806078, 3, 35792568, 3010349, 2387010102192469724605148123694256128, 2, 0, 53, 43, 0, 4696, 173, 44583, 1111111111111111111111111111111111111111111

Offset: 1

dead

A031214 Initial term of sequence An.

Original entry on oeis.org

0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 2, 2, 1, 2, 1, 1, 2, 1, 0, 1, 1, 1, 0, 1, 2, 8, 14, 4, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 0, 4, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1

Offset: 1

Jeff Burch

This ignores the offset and gives the first term of the actual entry.
Since the sequences in the OEIS occasionally change their initial terms (for editorial reasons), this is an especially ill-defined sequence! - N. J. A. Sloane, Jan 01 2005
Sequences like this are deprecated. - Joerg Arndt, Apr 16 2020

			A000001 begins 0,1,1,1,2,1,2,1,5,2,... so a(1) = 0 = a(31214).

PrimeFan, Esoteric Integer Sequences
PrimeFan, Esoteric Integer Sequences [Cached copy]
N. J. A. Sloane, Online Encyclopedia of Integer Sequences
Index entries for sequences whose definition involves A_n (or An).

Cf. A039928, A051070, A091967, A107357, A102288; also A000001, A000002, A000003, A000004, A000005, etc.

Data updated by Sean A. Irvine, Apr 16 2020

A051070 a(n) is the n-th term in sequence A_n, respecting the offset, or a(n) = -1 if A_n has fewer than n terms.

Original entry on oeis.org

1, 2, 1, 0, 2, 3, 0, 7, 8, 4, 63, 1, 316, 78, 16, 2048, 7652, 26627, 8, 24000, 232919, 1145406, 3498690007594650042368, 2058537, 58, 26, 27, 59, 9272780, 3, 69273668, 4870847, 2387010102192469724605148123694256128, 1, 1, -53, 43, 0, -4696, 173, 44583, 111111111111111111111111111111111111111111, 30402457, 668803781, 1134903170, 382443020332

Offset: 1

Robert G. Wilson v, Aug 23 2000

a(58) = A000058(58) = 192523...920807 (58669977298272603 digits) is too large to include in the b-file. - Pontus von Brömssen, May 19 2022
Comment from N. J. A. Sloane, Dec 26 2022 (Start)
Note that a(n) = -1 can arise in two ways: either A_n has fewer than n terms, or A_n has at least n terms, but its n-th term is -1.
Here is a summary of the terms with n <= 80.
a(n) = -1 occurs just twice, for n = 53 and 54, in both cases because the relevant New York subway lines do not have enough stops.
a(1) though a(65) are known, although a(58) = = 192523...920807 has 58669977298272603 digits.
a(66) is the first unknown value.
Also unknown for n <= 80 are a(67), a(72), a(74), a(75), a(76), and a(77) (counts of numbers <= 2^n represented by various quadratic forms; some of these do not even have b-files), and a(80), which like a(66) is a graph-theory question. (End)

			a(19) = 8 because A000019(19) = 8.
a(20) = 24000 because A000020(20) = 24000.

Seth A. Troisi, Table of n, a(n) for n = 1..57 (terms 1..48 from Pontus von Brömssen).
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 21.
Index entries for sequences whose definition involves A_n (or An).

See A091967, A107357, A102288 for other versions. See also A031214, A031135.

Cf. A000019, A000020, A000058.

for m from 1 do
  url:= sprintf("https://oeis.org/A%06d/b%06d.txt",m,m);
  S:= URL:-Get(url);
  L:= StringTools[Split](S,"\n");
  for t in L do
    g:= sscanf(t, "%d %d");
    if nops(g) = 2 and g[1] = m then
      a[m]:= g[2];
      break
    fi;
  od;
  if not assigned(a[m]) then break fi;
od:
seq(a[i],i=1..m-1); # Robert Israel, May 31 2015

Rechecked and 4 more terms added by N. J. A. Sloane, May 25 2005
a(36) and a(42) corrected and a(43) to a(46) added by Robert Israel, May 31 2015
Definition revised by N. J. A. Sloane, Nov 27 2016

A091967 a(n) is the n-th term of sequence A_n, ignoring the offset, or -1 if A_n has fewer than n terms.

Original entry on oeis.org

0, 2, 1, 0, 2, 3, 0, 6, 6, 4, 44, 1, 180, 42, 16, 1096, 7652, 13781, 8, 24000, 119779, 458561, 152116956851941670912, 1054535, -53, 26, 27, 59, 4806078, 2, 35792568, 3010349, 2387010102192469724605148123694256128, 2, 0, -53, 43, 0, -4097, 173, 37338, 111111111111111111111111111111111111111111, 30402457, 413927966

Offset: 1

Proposed by several people, including Jeff Burch and Michael Joseph Halm

sign

This version ignores the offset of A_n and just counts from the beginning of the terms shown in the OEIS entry.
Thus a(8) = 6 because A_8 begins 1,1,2,2,3,4,5,6,... [even though A_8(8) is really 7].
The value a(n) = -1 could arise in two different ways, but it will be easy to decide which. - N. J. A. Sloane, Nov 27 2016
From M. F. Hasler, Sep 22 2013: (Start)
The value of a(91967) can be chosen at will.
Note that this sequence may change if the initial terms in A_n are altered, which does happen from time to time, usually because of the addition of an initial term.
After a(47), currently unknown, the sequence continues with a(48) = A48(47) = 1497207322929, a(49) = A49(48) = unknown, a(50) = A50(49) = unknown, a(51) = A51(50) = 1125899906842625, a(52)=97, a(53) = -1 (since A000053 has only 29 terms). (End)
a(58) = A000058(57) = 138752...985443 (29334988649136302 digits) is too large to include in the b-file. - Pontus von Brömssen, May 21 2022

			a(1) = 0 since A000001 has offset 0, and begins with A000001(0) = 0.
a(26) = 26 because the 26th term of A000026 = 26.

Pontus von Brömssen, Table of n, a(n) for n = 1..57 (terms n = 1..46 from M. F. Hasler)
OEIS, List of finite sequences, sorted by A-number.
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
Index entries for sequences whose definition involves A_n (or An).

See A051070, A107357, A102288 for other versions.

Cf. A000001, A000002, A000003, A000004, A000005, A000006, A000007, A000008, A000009, A000010, A000011, A000012, A000013, A000014, A000015, etc.

Corrected and extended by Jud McCranie; further extended by N. J. A. Sloane and E. M. Rains, Dec 08 1998
Corrected and extended by N. J. A. Sloane, May 25 2005
a(26), a(36) and a(42) corrected by M. F. Hasler, Jan 30 2009
a(43) and a(44) added by Daniel Sterman, Nov 27 2016
a(1) corrected by N. J. A. Sloane, Nov 27 2016 at the suggestion of Daniel Sterman
Definition and comments changed by N. J. A. Sloane, Nov 27 2016

A102288 a(n) = 1 + (the n-th term in sequence A_n, ignoring the offset), or a(n) = -1 if A_n has fewer than n terms.

Original entry on oeis.org

1, 3, 2, 1, 3, 4, 1, 7, 7, 5, 45, 2, 181, 43, 17, 1097, 7653, 13782, 9, 24001, 119780, 458562, 152116956851941670913, 1054536, -52, 27, 28, 60, 4806079, 3, 35792569, 3010350, 2387010102192469724605148123694256129, 3, 1, -52, 44, 1, -4096, 174, 37339, 111111111111111111111111111111111111111112, 30402458, 413927967

Offset: 1

Alexandre Wajnberg, Feb 19 2005

sign

a(n) = A091967(n) + 1, except when A_n has fewer than n terms, in which case a(n) = -1. Of course this means that a value a(n) = -1 could arise in two different ways, but it will be easy to decide which. - N. J. A. Sloane, Nov 27 2016
What is a(102288)?!
See A091967 and A051070 for much more about this type of sequence. See A107357 for the variant which respects the offset of A_n (and therefore isn't affected when a sequence is completed by missing initial values).
The definition of this sequence is used in the traditional 'diagonal' proof that there are uncountably many integer sequences. - Simon Nickerson (simonn(AT)maths.bham.ac.uk), Jun 28 2005
The term a(102288) has no possible value according to the present definition, so the definition of this term should be changed, including the possibility that the sequence is defined to be finite, with fewer than 102288 terms. (In that case, the (former, impossible) definition which would say that a(102288) = -1 because A102288 has fewer than 102288 terms, does not apply.) - The term a(47) is currently unknown, since A000047 is known only up to n = 35. - M. F. Hasler, Jan 20 2017
I disagree with the previous comment! I prefer the present, deliberately paradoxical, definition. - N. J. A. Sloane, Jan 20 2017

			a(53) = -1 since A000053 has only 29 terms.

M. F. Hasler, Table of n, a(n) for n = 1..46
Index entries for sequences whose definition involves A_n (or An).

a(n) = A091967(n) + 1. See also A051070, A107357 (the same but respecting the offset).

Corrected and extended by N. J. A. Sloane, May 25 2005
Offset corrected by M. F. Hasler, Sep 22 2013
Corrected and extended by Daniel Sterman, Nov 27 2016
Definition revised by N. J. A. Sloane, Nov 27 2016
a(1) fixed by Daniel Sterman, Nov 28 2016
a(26) corrected by M. F. Hasler, Jan 20 2017

A053169 A paradoxical sequence: a positive integer n is in this sequence if and only if n is not in sequence A_n in the database.

Original entry on oeis.org

4, 7, 9, 11, 12, 13, 15, 17, 18, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 60, 61, 63, 64, 65, 66, 67, 68, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100

Offset: 1

Miklos Szabo (mike(AT)ludens.elte.hu), N. J. A. Sloane, Feb 29 2000

"Not in sequence A_n" means not in the full list of terms, not simply in the list of terms visible in the entry.

The paradox is of course: is 53169 in this sequence?

			Sequence A000001 contains 1, so 1 is not in the sequence; A000002 contains 2, so 2 is not in the sequence; ...

Smullyan, Raymond M, What is the name of this book? : The riddle of Dracula and other logical puzzles, Englewood Cliffs, NJ : Prentice-Hall, c1978, see puzzle 163.

Index entries for sequences whose definition involves A_n (or An).

Cf. A107357.

Complement of A053873.

Thanks to Alexander Hulpke for the information that 19 is in A000019.

Extended to n=100 by N. J. A. Sloane, May 26 2007

A031135 Incorrect version of A091967.

Original entry on oeis.org

1, 2, 1, 0, 2, 3, 0, 6, 8, 4, 63, 1, 316, 42, 16, 2048, 7652, 13781, 8, 24000, 11977, 458561, 152116956851941670912, 1054535, 53, 26, 27, 59, 4806078, 3, 35792568, 3010349, 2387010102192469724605148123694256128, 2, 0, 53, 43, 0

Offset: 1

dead

Probably because of changes in the offsets of certain sequences, this is now incorrect. See A051070, A091967, A107357, A102288 for better versions.

cp's OEIS Frontend

A037181 Incorrect version of A107357.

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A031214 Initial term of sequence An.

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A051070 a(n) is the n-th term in sequence A_n, respecting the offset, or a(n) = -1 if A_n has fewer than n terms.

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A091967 a(n) is the n-th term of sequence A_n, ignoring the offset, or -1 if A_n has fewer than n terms.

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A102288 a(n) = 1 + (the n-th term in sequence A_n, ignoring the offset), or a(n) = -1 if A_n has fewer than n terms.

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A053169 A paradoxical sequence: a positive integer n is in this sequence if and only if n is not in sequence A_n in the database.

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A031135 Incorrect version of A091967.

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