A100266 Primes of the form x^16 + y^16.

2, 65537, 4338014017, 2973697798081, 36054040477057, 314707907280257, 184884411482927041, 665698084159890497, 675416609183179841, 2177953490397261761, 8746361693522261761, 18492693803573123777

Offset

1,1

Comments

The Mathematica program generates numbers of the form x^16 + y^16 in order of increasing magnitude; it accepts a number when it is prime.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Generalized Fermat Number.

Mathematica

n=4; 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]]; !PrimeQ[p]]; p, {15}]
q=16; lst={}; Do[Do[p=n^q+m^q; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 5!}], {m, 0, 5!}]; lst; Length[lst]; Take[Union[lst], 55] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2009 *)
Union[Select[Total[#^16]&/@Tuples[Range[20], 2], PrimeQ]] (* Harvey P. Dale, Nov 03 2013 *)

Crossrefs

Cf. A100267 (primes of the form x^32 + y^32), A006686 (primes of the form x^8 + y^8), A002645 (primes of the form x^4 + y^4), A002313 (primes of the form x^2 + y^2).

Sequence in context: A051833 A213619 A060895 * A272137 A272248 A195003

Adjacent sequences: A100263 A100264 A100265 * A100267 A100268 A100269

Keyword

nonn

Author

T. D. Noe, Nov 11 2004

Status

approved