OFFSET
1,1
COMMENTS
The first Mathematica program generates numbers of the form x^4 + y^4 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.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Generalized Fermat Number
MATHEMATICA
n=2; 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, {40}]
With[{nn=40}, Select[Union[Transpose[Select[Total/@{#^4, #^2, #}&/@ Tuples[ Range[nn], 2], AllTrue[#, PrimeQ]&]][[1]]], #<=nn^4+1&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 23 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Nov 11 2004
STATUS
approved