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.

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

Author

Robert G. Wilson v, Aug 23 2000

Keywords

• easy
• sign

Comments

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)

Examples

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

Links

• 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).

Crossrefs

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

Cf. A000019, A000020, A000058.

Programs

Maple

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

Extensions

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