|
%I #13 Feb 21 2023 06:17:36
%S 2,257,65537,2724909545357921,3282116715437377,40213879071634241,
%T 147578912575757441,303879829574456257,697576026529536481,
%U 1316565220482548321,2860283484326400961,4080251077774711937
%N Primes of the form x^8 + y^8 with x^4 + y^4, x^2 + y^2 and x+y also prime.
%C The Mathematica program generates numbers of the form x^8 + y^8 in order of increasing magnitude; it accepts a number when all the x^2^k + y^2^k are prime for k=0,1,2,3.
%H Vincenzo Librandi, <a href="/A100269/b100269.txt">Table of n, a(n) for n = 1..100</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GeneralizedFermatNumber.html">Generalized Fermat Number</a>.
%t n=3; pwr=2^n; xmax=2; r=Range[xmax]; num=r^pwr+r^pwr; Table[While[p=Min[num]; x=Position[num, p][[1, 1]]; y=r[[x]]; r[[x]]++; num[[x]]=x^pwr+r[[x]]^pwr; If[x==xmax, xmax++; AppendTo[r, xmax+1]; AppendTo[num, xmax^pwr+(xmax+1)^pwr]]; allPrime=True; k=0; While[k<=n&&allPrime, allPrime=PrimeQ[x^2^k+y^2^k]; k++ ]; !allPrime]; p, {20}]
%Y Cf. A099332, A100268, A100270.
%K nonn
%O 1,1
%A _T. D. Noe_, Nov 11 2004
|
