A291206 Semi-octavan primes: primes of the form x^4 + y^8.

2, 17, 257, 337, 881, 1297, 2657, 6577, 10657, 14897, 16561, 28817, 65537, 65617, 66161, 80177, 83777, 149057, 160001, 166561, 260017, 280097, 331777, 391921, 394721, 411361, 463537, 596977, 614657, 621217, 847601, 1055137, 1336337, 1342897, 1682017, 1763137

Offset: 1

Author

Charles R Greathouse IV, Aug 21 2017

Keywords

• nonn

Examples

			a(1) = 1^4 + 1^8 = 2.
a(2) = 2^4 + 1^8 = 17.
a(3) = 1^4 + 2^8 = 257.
a(4) = 3^4 + 2^8 = 337.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• A. J. C. Cunningham, High quartan factorisations and primes, Messenger of Mathematics 36 (1907), pp. 145-174.

Crossrefs

Subsequence of A002645 and hence of A028916. A006686 is a subsequence.

Programs

Mathematica

Take[Select[Flatten[Table[x^4+y^8,{x,40},{y,40}]],PrimeQ]//Union,40] (* Harvey P. Dale, May 01 2025 *)

PARI

list(lim)=my(v=List([2]),x4,t); for(x=1, sqrtnint(lim\=1,4), x4=x^4; forstep(y=x%2+1, sqrtnint(lim-x4,8), 2, if(isprime(t=x4+y^8), listput(v, t)))); Set(v)