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A277125
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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.
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0
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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sign,hard,more,bref
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AUTHOR
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STATUS
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approved
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