A122703 Primes of the form p^2 + q^7 where p and q are primes.

137, 823547, 271818611111, 9974730326005061, 630634881591804953, 32525450580470426321, 2169562730596120989977, 3863897579789788264121, 122288345645958900577487, 680203568668250740574183, 3167337505302652506404471, 6421072852468062867774503, 8417887306491957134503937, 21307550075749197394472141

Offset

1,1

Comments

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.

Links

Robert Israel, Table of n, a(n) for n = 1..5449

Formula

{a(n)} = {p^2 + q^7 in A000040 where p and q are in A000040}.

Example

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.

Maple

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

Crossrefs

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

Keyword

nonn

Author

Jonathan Vos Post, Sep 22 2006

Extensions

More terms from Robert Israel, Jan 24 2018

Status

approved