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A122703
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Primes of the form p^2 + q^7 where p and q are primes.
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1
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137, 823547, 271818611111, 9974730326005061, 630634881591804953, 32525450580470426321, 2169562730596120989977, 3863897579789788264121, 122288345645958900577487, 680203568668250740574183, 3167337505302652506404471, 6421072852468062867774503, 8417887306491957134503937, 21307550075749197394472141
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OFFSET
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1,1
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COMMENTS
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p and q cannot both be odd. Thus p=2 or q=2. After 3^2 + 2^7 = 137, all solutions are of the form 2^2 + q^7.
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..5449
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FORMULA
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{a(n)} = {p^2 + q^7 in A000040 where p and q are in A000040}.
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EXAMPLE
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a(1) = 3^2 + 2^7 = 137.
a(2) = 2^2 + 7^7 = 823547.
a(3) = 2^2 + 43^7 = 271818611111.
a(4) = 2^2 + 193^7 = 9974730326005061.
a(5) = 2^2 + 349^7 = 630634881591804953.
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MAPLE
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N:= 10^30: # to get all terms <= N
A:= select(isprime, {137, seq(2^2 + q^7, q = select(isprime, [2, seq(i, i=3..floor((N-4)^(1/7)), 2)]))}):
sort(convert(A, list)); # Robert Israel, Jan 24 2018
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CROSSREFS
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Cf. A000040, A045700 (Primes of form p^2+q^3 where p and q are primes).
Sequence in context: A134874 A064104 A300407 * A200335 A351237 A292094
Adjacent sequences: A122700 A122701 A122702 * A122704 A122705 A122706
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post, Sep 22 2006
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EXTENSIONS
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More terms from Robert Israel, Jan 24 2018
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STATUS
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approved
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