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A100268 Primes of the form x^4 + y^4 with x^2 + y^2 and x+y also prime. 3
2, 17, 97, 257, 641, 1297, 4177, 4721, 12401, 15937, 16561, 38561, 65537, 83537, 89041, 105601, 140321, 160081, 204481, 283937, 284881, 384817, 391921, 411361, 462097, 471617, 531457, 643217, 824641, 838561, 1049201, 1089841, 1342897 (list; graph; refs; listen; history; text; internal format)
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

Cf. A099332, A100269, A100270.

Sequence in context: A219757 A297727 A002645 * A163790 A129123 A109724

Adjacent sequences:  A100265 A100266 A100267 * A100269 A100270 A100271

KEYWORD

nonn

AUTHOR

T. D. Noe, Nov 11 2004

STATUS

approved

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Last modified June 15 20:50 EDT 2019. Contains 324145 sequences. (Running on oeis4.)