A277125 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.

-13, -5, 1, -3

Offset

1,1

Comments

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).

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).

Links

Table of n, a(n) for n=1..4.

R. Scott and R. Styer, On p^x - q^y = c and related three term exponential Diophantine equations with prime bases, Journal of Number Theory, Vol. 105, No. 2 (2004), 212-234.

Example

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.

Crossrefs

Cf. A001220.

Sequence in context: A366253 A226376 A222165 * A249267 A123172 A010218

Adjacent sequences: A277122 A277123 A277124 * A277126 A277127 A277128

Keyword

sign,hard,more,bref

Author

Felix Fröhlich, Oct 31 2016

Status

approved