cp's OEIS Frontend

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.

%I A051070 #82 Jan 13 2023 18:58:02
%S A051070 1,2,1,0,2,3,0,7,8,4,63,1,316,78,16,2048,7652,26627,8,24000,232919,
%T A051070 1145406,3498690007594650042368,2058537,58,26,27,59,9272780,3,
%U A051070 69273668,4870847,2387010102192469724605148123694256128,1,1,-53,43,0,-4696,173,44583,111111111111111111111111111111111111111111,30402457,668803781,1134903170,382443020332
%N 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.
%C A051070 a(58) = A000058(58) = 192523...920807 (58669977298272603 digits) is too large to include in the b-file. - _Pontus von Brömssen_, May 19 2022
%C A051070 Comment from _N. J. A. Sloane_, Dec 26 2022 (Start)
%C A051070 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.
%C A051070 Here is a summary of the terms with n <= 80.
%C A051070 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.
%C A051070 a(1) though a(65) are known, although a(58) = = 192523...920807 has 58669977298272603 digits.
%C A051070 a(66) is the first unknown value.
%C A051070 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)
%H A051070 Seth A. Troisi, <a href="/A051070/b051070.txt">Table of n, a(n) for n = 1..57</a> (terms 1..48 from Pontus von Brömssen).
%H A051070 N. J. A. Sloane, <a href="http://neilsloane.com/doc/sg.txt">My favorite integer sequences</a>, in Sequences and their Applications (Proceedings of SETA '98).
%H A051070 N. J. A. Sloane, <a href="https://arxiv.org/abs/2301.03149">"A Handbook of Integer Sequences" Fifty Years Later</a>, arXiv:2301.03149 [math.NT], 2023, p. 21.
%H A051070 <a href="/index/Se#selfies">Index entries for sequences whose definition involves A_n (or An)</a>.
%e A051070 a(19) = 8 because A000019(19) = 8.
%e A051070 a(20) = 24000 because A000020(20) = 24000.
%p A051070 for m from 1 do
%p A051070   url:= sprintf("https://oeis.org/A%06d/b%06d.txt",m,m);
%p A051070   S:= URL:-Get(url);
%p A051070   L:= StringTools[Split](S,"\n");
%p A051070   for t in L do
%p A051070     g:= sscanf(t, "%d %d");
%p A051070     if nops(g) = 2 and g[1] = m then
%p A051070       a[m]:= g[2];
%p A051070       break
%p A051070     fi;
%p A051070   od;
%p A051070   if not assigned(a[m]) then break fi;
%p A051070 od:
%p A051070 seq(a[i],i=1..m-1); # _Robert Israel_, May 31 2015
%Y A051070 See A091967, A107357, A102288 for other versions. See also A031214, A031135.
%Y A051070 Cf. A000019, A000020, A000058.
%K A051070 easy,sign
%O A051070 1,2
%A A051070 _Robert G. Wilson v_, Aug 23 2000
%E A051070 Rechecked and 4 more terms added by _N. J. A. Sloane_, May 25 2005
%E A051070 a(36) and a(42) corrected and a(43) to a(46) added by _Robert Israel_, May 31 2015
%E A051070 Definition revised by _N. J. A. Sloane_, Nov 27 2016