A122702 Primes of the form p^3 + q^5 where p and q are primes.

59, 157, 251, 24421, 161059, 2248123, 6436351, 6967903, 15813283, 20511157, 22188073, 58863901, 86938339, 90518881, 131872261, 263374753, 440711113, 553387693, 865523209, 1095912823, 1194390013, 1524845983, 1573037779, 2521008913, 2979767551, 3327970189

Offset

1,1

Comments

p and q cannot both be odd. Thus p=2 or q=2.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

{a(n)} = {p^3 + q^5 in A000040 where p and q are in A000040}.

Example

a(1) = 3^3 + 2^5 = 59.
a(2) = 5^3 + 2^5 = 157.
a(3) = 2^3 + 3^5 = 251.
a(4) = 29^3 + 2^5 = 24421.

Maple

N:= 10^10: # to get all terms <= N
A:= select(isprime, {seq(2^3 + q^5, q = select(isprime, [2, seq(i, i=3..floor((N-8)^(1/5)), 2)])),
seq(2^5 + q^3, q = select(isprime, [2, seq(i, i=3..floor((N-2^5)^(1/3)), 2)]))}):
sort(convert(A, list)); # Robert Israel, Jan 23 2018

Mathematica

With[{nn=10^8}, Union[Select[Join[Prime[Range[Floor[Power[nn, (5)^-1]]]]^5+ 8, Prime[Range[Floor[Power[nn, (3)^-1]]]]^3+32], PrimeQ]]] (* Harvey P. Dale, Nov 26 2011 *)

Crossrefs

Cf. A000040, A045700 (Primes of form p^2+q^3 where p and q are primes).

Sequence in context: A140687 A118154 A033671 * A142422 A255352 A044391

Adjacent sequences: A122699 A122700 A122701 * A122703 A122704 A122705

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 22 2006

Extensions

More terms from Harvey P. Dale, Nov 26 2011

Status

approved