A305538 a(n) is the smallest positive generalized pentagonal number such that A001318(n) - a(n) is twice a generalized pentagonal number.

1, 3, 2, 1, 8, 2, 5, 10, 7, 5, 18, 7, 12, 20, 3, 12, 5, 1, 22, 3, 10, 22, 13, 8, 35, 11, 20, 35, 2, 18, 5, 22, 33, 1, 12, 31, 16, 8, 49, 12, 25, 47, 30, 21, 2, 26, 41, 66, 11, 37, 16, 5, 60, 10, 27, 56, 33, 21, 82, 27, 46, 78, 7, 40, 13, 47, 68, 5, 26, 62, 33

Offset

3,2

Comments

Such a number exists for n >= 3 due to a theorem of Enge, Hart and Johansson (see the link, p. 11).

Links

Peter Luschny, Table of n, a(n) for n = 3..1000

Andreas Enge, William Hart and Fredrik Johansson, Short addition sequences for theta functions, Journal of Integer Sequences, Vol. 21 (2018), Article 18.2.4. Also available as arXiv:1608.06810 [math.NT].

Example

(A001318(328) - a(328))/2 = (40426 - 174)/2 = 20126 = A001318(231).

Crossrefs

Cf. A001318, A305539.

Sequence in context: A196842 A158474 A090452 * A370527 A193924 A110439

Adjacent sequences: A305535 A305536 A305537 * A305539 A305540 A305541

Keyword

nonn

Author

Peter Luschny, Jun 04 2018

Status

approved