A122710 Primes of the form p^2 + q^8 where p and q are primes.

281, 617, 1097, 1217, 5297, 10457, 17417, 19577, 23057, 32297, 39857, 44777, 52697, 58337, 72617, 167537, 192977, 212777, 241337, 249257, 383417, 398417, 502937, 517217, 564257, 704177, 830177, 885737, 943097, 982337, 1018337, 1038617, 1079777, 1442657, 1515617, 1560257, 1692857, 1745297, 1985537

Offset

1,1

Comments

p and q cannot both be odd. Thus p=2 or q=2. There are no primes of the form 2^2 + q^8 (consider divisibility by 5). Hence all solutions are of the form p^2 + 2^8 and are congruent to 7 mod 10.

Links

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

Formula

{a(n)} = {p^2 + q^8 in A000040 where p and q are in A000040}.

Example

a(1) = 5^2 + 2^8 = 281.
a(2) = 19^2 + 2^8 = 617.
a(3) = 29^2 + 2^8 = 1097.

Maple

N:= 10^6: # to get terms up to N
select(isprime, [seq(2^8 + p^2, p = select(isprime, [5, seq(seq(10*i+j, j=[1, 9]), i=1..isqrt(N-2^8)/10)]))]); # Robert Israel, Jan 24 2018

Crossrefs

Cf. A000040, A045700 (of form p^2+q^3), A122617 (of form p^3+q^4).

Sequence in context: A142397 A142546 A163184 * A161191 A108836 A295983

Adjacent sequences: A122707 A122708 A122709 * A122711 A122712 A122713

Keyword

nonn

Author

Jonathan Vos Post, Sep 23 2006

Extensions

More terms from Robert Israel, Jan 24 2018

Status

approved