A122715 Primes of the form p^2 + q^9 where p and q are primes.

521, 19687, 40353611, 27206534396294951, 58871586708267917, 977752464192721105849427, 1733003264116942402576542827, 24847921085939626319928324473, 114264841877247135195655381697

Offset

1,1

Comments

p and q cannot both be odd. Thus p=2 or q=2. There are no primes of the form 2^9 + q^2 other than 3^2 + 2^9 = 521. Hence all solutions are of the form 2^2 + q^9.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

{a(n)} = {p^2 + q^9 in A000040 where p and q are in A000040}.

Example

a(1) = 3^2 + 2^9 = 521.
a(2) = 2^2 + 3^9 = 19687.
a(3) = 2^2 + 7^9 = 40353611.
a(4) = 2^2 + 67^9 = 27206534396294951.
a(5) = 2^2 + 73^9 = 58871586708267917.
a(6) = 2^2 + 453^9 = 803311192691904837821737.

Mathematica

s = {521}; Do[ pq = Prime@p^9 + 4; If[ PrimeQ@pq, AppendTo[s, pq]], {p, 300}]; s (* Robert G. Wilson v *)
Join[{521}, Select[Prime[Range[300]]^9+4, PrimeQ]] (* Harvey P. Dale, Apr 11 2018 *)

Crossrefs

Cf. A000040, A045700 Primes of form p^2+q^3 where p and q are prime, A122617 Primes of form p^3+q^4 where p and q are primes.

Sequence in context: A138063 A324630 A167734 * A153180 A173656 A015291

Adjacent sequences: A122712 A122713 A122714 * A122716 A122717 A122718

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 23 2006

Extensions

More terms from Robert G. Wilson v, Sep 26 2006

Status

approved