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%I #44 Mar 25 2018 08:21:17
%S -13,-5,1,-3
%N Integers d such that the Diophantine equation p^x - 2^y = d has more than one solution in positive integers (x, y), where p is a positive prime number. Terms sorted first after increasing size of p, then in increasing order.
%C Let b(n) be the sequence giving the values of the primes p corresponding to a(n). b(1)-b(4) are 3, 3, 3, 5 (cf. (ii) and (iv) in Scott, Styer, 2004).
%C Any other pair (p, d) must be of the form (A001220(i), d) for some i > 2 (cf. Corollary to Theorem 2 in Scott, Styer, 2004).
%H R. Scott and R. Styer, <a href="http://dx.doi.org/10.1016/j.jnt.2003.11.008">On p^x - q^y = c and related three term exponential Diophantine equations with prime bases</a>, Journal of Number Theory, Vol. 105, No. 2 (2004), 212-234.
%e Two solutions (x, y) of the Diophantine equation 5^x - 2^y = -3 are (1, 3) and (3, 7), so -3 is a term of the sequence.
%Y Cf. A001220.
%K sign,hard,more,bref
%O 1,1
%A _Felix Fröhlich_, Oct 31 2016
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