Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #21 Jul 09 2019 02:36:19
%S 1,5,7,13,23
%N The only nonunique differences between powers of 3 and 2.
%C The sequence is finite, this fact is a theorem in [Bennet2004].
%C 1 = 3-2 = 3^2-2^3 = 2^2-3.
%C 5 = 3^2-2^2 = 2^3-3 = 2^5 - 3^3.
%C 7 = 2^4-3^2 = 3^2 - 2.
%C 13 = 2^4-3 = 2^8 - 3^5.
%C 23 = 3^3 - 2^2 = 2^5 - 3^2.
%H M. A. Bennett, <a href="http://www.math.ubc.ca/~bennett/B-Pillai.pdf">Pillai's conjecture revisited</a>, J. Number Theory 98 (2003), 228-235.
%H Douglas Edward Iannucci, <a href="https://arxiv.org/abs/1907.03347">On duplicate representations as 2^x+3^y for nonnegative integers x and y</a>, arXiv:1907.03347 [math.NT], 2019. Mentions this sequence.
%F A219551(a(n)) > 1. - _Jonathan Sondow_, Dec 10 2012
%Y Cf. A053289, A074981, A076438, A219551.
%K nonn,bref,fini,full
%O 1,2
%A _Gottfried Helms_, Feb 15 2012