This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A219551 #20 Mar 06 2017 19:35:00
%S A219551 0,3,0,0,0,3,0,2,0,0,0,1,0,2,0,0,0,1,0,1,0,0,0,2,0,1,0,0,0,1,0
%N A219551 Number of positive integer solutions to the equation |2^x - 3^y| = n.
%C A219551 Pillai (1931) proved that a(n) is finite for all n.
%C A219551 Hershfeld (1936) computed a(n) for n <= 10 and proved that a(n) <= 2 for all large n.
%C A219551 Stroeker and Tijdeman (1982) proved that a(n) <= 2 for all n > 13.
%C A219551 For additional comments, references, and links, see the crossrefs.
%C A219551 a(n) <= 1 except for n=1, 5, 7, 13, 23: see e,g, Bennett (2003). - _Robert Israel_, Mar 06 2017
%D A219551 S. Pillai, On the inequality 0 < a^x - b^y <= n, Journal Indian Math. Soc., 19 (1931), 1-11.
%D A219551 R. J. Stroeker and R. Tijdeman, Diophantine equations, Computational methods in number theory, Part 2, Math. Cent. Tracts, 155 (1982), 321-369.
%H A219551 M. A. Bennett, <a href="http://dx.doi.org/10.4153/CJM-2001-036-6">On Some Exponential Equations of S. S. Pillai</a>, Canad. J. Math. 53 (2001), 897-922.
%H A219551 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 A219551 A. Herschfeld, <a href="https://doi.org/10.1090/S0002-9904-1936-06275-0">The equation 2^x - 3^y = d</a>, Bull. Amer. Math. Soc., 42 (1936), 231-234.
%H A219551 M. Waldschmidt, <a href="http://arxiv.org/abs/0908.4031">Perfect Powers: Pillai's works and their developments</a>, arXiv:0908.4031 [math.NT], 2009.
%F A219551 a(2n) = a(3n) = 0.
%F A219551 a(n) <= 2 for n > 13.
%e A219551 1 = 2^2 - 3 = 3 - 2 = 3^2 - 2^3.
%e A219551 5 = 2^3 - 3 = 2^5 - 3^3 = 3^2 - 2^2.
%e A219551 7 = 2^4 - 3^2 = 3^2 - 2.
%e A219551 23 = 2^5 - 3^2 = 3^3 - 2^2 and a(n) <= 2 for n > 13, so a(23) = 2.
%t A219551 Clear[seq]; seq[m_] := seq[m] = (Clear[a]; a[_] = 0; Do[n = Abs[2^x - 3^y]; a[n] = a[n] + 1, {x, 1, m}, {y, 1, m}]; Table[a[n], {n, 0, 10}]); seq[m = 1]; While[seq[m] != seq[m - 1], m = 2*m]; A219551 = seq[m] (* _Jean-François Alcover_, Dec 13 2012 *)
%Y A219551 Cf. A053289, A074981, A076438, A207079.
%K A219551 nonn,more
%O A219551 0,2
%A A219551 _Jonathan Sondow_, Dec 09 2012
%E A219551 a(11) - a(30) from _Robert Israel_, Mar 06 2017