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 A100266 Primes of the form x^16 + y^16. 14
 2, 65537, 4338014017, 2973697798081, 36054040477057, 314707907280257, 184884411482927041, 665698084159890497, 675416609183179841, 2177953490397261761, 8746361693522261761, 18492693803573123777 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 8 15:23 EST 2023. Contains 367680 sequences. (Running on oeis4.)