login
A305538
a(n) is the smallest positive generalized pentagonal number such that A001318(n) - a(n) is twice a generalized pentagonal number.
2
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
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
Sequence in context: A196842 A158474 A090452 * A370527 A193924 A110439
KEYWORD
nonn
AUTHOR
Peter Luschny, Jun 04 2018
STATUS
approved