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

Author

Peter Luschny, Jun 04 2018

Keywords

• nonn

Comments

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

Examples

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

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].

Crossrefs

Cf. A001318, A305539.