A290780 Half-octavan primes: primes of the form (x^8 + y^8)/2.

198593, 21523361, 107182721, 407865361, 429388721, 3487882001, 11979660241, 39155495921, 84785726833, 141217650641, 141321947681, 250123401793, 253611085201, 289278699121, 391337974721, 426445714033, 426448401121

Offset: 1

Author

Charles R Greathouse IV, Aug 20 2017

Keywords

• nonn

Examples

			a(1) = (5^8 + 3^8)/2 = 198593.
a(2) = (9^8 + 1^8)/2 = 21523361.
a(3) = (11^8 + 3^8)/2 = 107182721.
a(4) = (13^8 + 1^8)/2 = 407865361.
a(5) = (13^8 + 9^8)/2 = 429388721.
		

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

Cf. A006686, A002646.

Programs

Maple

N:= 10^12: # to get all terms <= N
sort(convert(select(isprime, {seq(seq((x^8+y^8)/2, y= (x mod 2)..min(x,floor((2*N-x^8)^(1/8))),2),x=1..floor((2*N)^(1/8)))}),list)); # Robert Israel, Aug 21 2017

Mathematica

Sort[Select[Total/@(Union[Sort/@Tuples[Range[0, 50], 2]]^8)/2, PrimeQ]] (* or *) lst={};Do[If[PrimeQ[(a^8 + b^8) / 2], AppendTo[lst, (a^8 + b^8) / 2]], {a, 100}, {b, a, 100}]; Sort[lst] (* Vincenzo Librandi, Aug 21 2017 *)

PARI

list(lim)=my(v=List(),x8,t); forstep(x=1,sqrtnint(lim\=1,8),2, x8=x^8; forstep(y=1,min(sqrtnint(lim-x8,8), x-1),2, if(isprime(t=(x8+y^8)/2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Aug 20 2017