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 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 (list; graph; refs; listen; history; text; internal format)
 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 * A193924 A110439 A327917 Adjacent sequences:  A305535 A305536 A305537 * A305539 A305540 A305541 KEYWORD nonn AUTHOR Peter Luschny, Jun 04 2018 STATUS approved

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Last modified January 25 01:49 EST 2020. Contains 331229 sequences. (Running on oeis4.)