A102288 - OEIS

%I #36 Dec 25 2022 19:54:13

%S 1,3,2,1,3,4,1,7,7,5,45,2,181,43,17,1097,7653,13782,9,24001,119780,

%T 458562,152116956851941670913,1054536,-52,27,28,60,4806079,3,35792569,

%U 3010350,2387010102192469724605148123694256129,3,1,-52,44,1,-4096,174,37339,111111111111111111111111111111111111111112,30402458,413927967

%N 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.

%C 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

%C What is a(102288)?!

%C 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).

%C 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

%C 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

%C I disagree with the previous comment! I prefer the present, deliberately paradoxical, definition. - _N. J. A. Sloane_, Jan 20 2017

%H M. F. Hasler, <a href="/A102288/b102288.txt">Table of n, a(n) for n = 1..46</a>

%H <a href="/index/Se#selfies">Index entries for sequences whose definition involves A_n (or An)</a>.

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

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

%K sign

%O 1,2

%A _Alexandre Wajnberg_, Feb 19 2005

%E Corrected and extended by _N. J. A. Sloane_, May 25 2005

%E Offset corrected by _M. F. Hasler_, Sep 22 2013

%E Corrected and extended by _Daniel Sterman_, Nov 27 2016

%E Definition revised by _N. J. A. Sloane_, Nov 27 2016

%E a(1) fixed by _Daniel Sterman_, Nov 28 2016

%E a(26) corrected by _M. F. Hasler_, Jan 20 2017