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%I #13 Jun 06 2018 08:28:18
%S 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,
%T 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,
%U 10,27,56,33,21,82,27,46,78,7,40,13,47,68,5,26,62,33
%N a(n) is the smallest positive generalized pentagonal number such that A001318(n) - a(n) is twice a generalized pentagonal number.
%C Such a number exists for n >= 3 due to a theorem of Enge, Hart and Johansson (see the link, p. 11).
%H Peter Luschny, <a href="/A305538/b305538.txt">Table of n, a(n) for n = 3..1000</a>
%H Andreas Enge, William Hart and Fredrik Johansson, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL21/Enge/enge1.html">Short addition sequences for theta functions</a>, Journal of Integer Sequences, Vol. 21 (2018), Article 18.2.4. Also available as <a href="http://arxiv.org/abs/1608.06810">arXiv:1608.06810</a> [math.NT].
%e (A001318(328) - a(328))/2 = (40426 - 174)/2 = 20126 = A001318(231).
%Y Cf. A001318, A305539.
%K nonn
%O 3,2
%A _Peter Luschny_, Jun 04 2018
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