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.

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

1,2

Comments

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

Links

M. F. Hasler, Table of n, a(n) for n = 1..46

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

Example

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

Crossrefs

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

Sequence in context: A205838 A238583 A238556 * A081248 A214636 A318582

Adjacent sequences: A102285 A102286 A102287 * A102289 A102290 A102291

Keyword

sign

Author

Alexandre Wajnberg, Feb 19 2005

Extensions

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

Status

approved