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The only nonunique differences between powers of 3 and 2.
5

%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