A091967 -id:A091967 - cp's OEIS frontend

A031135 Incorrect version of A091967.

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.

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

A107357 a(n) = 1 + A_n(n), or a(n) = -1 if sequence A_n is not defined up to index n.

Original entry on oeis.org

2, 3, 2, 1, 3, 4, 1, 8, 9, 5, 64, 2, 317, 79, 17, 2049, 7653, 26628, 9, 24001, 232920, 1145407, 3498690007594650042369, 2058538, 59, 27, 28, 60, 9272781, 4, 69273669, 4870848, 2387010102192469724605148123694256129, 2, 2, -52, 44, 1, -4695, 174, 44584, 111111111111111111111111111111111111111112, 30402458, 668803782, 1134903171, 382443020333

Offset: 1

N. J. A. Sloane, May 25 2005

sign

What is a(107357)?

See A051070, A091967, A102288 for more about this type of sequence.

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).

a(n) = A051070(n) + 1 (except when A_n has fewer than n terms). See also A091967 and A102288 (the same but ignoring the offset).

Definition revised by N. J. A. Sloane, Nov 27 2016
Definition rephrased by M. F. Hasler, Jan 20 2017
Corrected a(36) and a(42), extended to a(46) by M. F. Hasler, Jan 21 2017

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

cp's OEIS Frontend

A031135 Incorrect version of A091967.

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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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A107357 a(n) = 1 + A_n(n), or a(n) = -1 if sequence A_n is not defined up to index n.

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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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