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 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. 0
 -13, -5, 1, -3 (list; graph; refs; listen; history; text; internal format)
 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 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: A046734 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

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Last modified May 29 04:33 EDT 2020. Contains 334697 sequences. (Running on oeis4.)