OFFSET
1,1
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.
EXAMPLE
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.
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Charles R Greathouse IV, Aug 20 2017
STATUS
approved