A291206 - OEIS

%I #17 Feb 13 2020 00:12:27

%S 2,17,257,337,881,1297,2657,6577,10657,14897,16561,28817,65537,65617,

%T 66161,80177,83777,149057,160001,166561,260017,280097,331777,391921,

%U 394721,411361,463537,596977,614657,621217,847601,1055137,1336337,1342897,1682017,1763137

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

%H Charles R Greathouse IV, <a href="/A291206/b291206.txt">Table of n, a(n) for n = 1..10000</a>

%H A. J. C. Cunningham, <a href="/wiki/File:High_quartan_factorisations_and_primes.pdf">High quartan factorisations and primes</a>, Messenger of Mathematics 36 (1907), pp. 145-174.

%e a(1) = 1^4 + 1^8 = 2.

%e a(2) = 2^4 + 1^8 = 17.

%e a(3) = 1^4 + 2^8 = 257.

%e a(4) = 3^4 + 2^8 = 337.

%o (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)

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

%K nonn

%O 1,1

%A _Charles R Greathouse IV_, Aug 21 2017