|
Search: id:A100268
|
|
|
| A100268 |
|
Primes of the form x^4 + y^4 with x^2 + y^2 and x+y also prime. |
|
+0
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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
The 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
|
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}]
|
|
CROSSREFS
|
Cf. A099332, A100269, A100270.
Adjacent sequences: A100265 A100266 A100267 this_sequence A100269 A100270 A100271
Sequence in context: A053786 A081744 A002645 this_sequence A129123 A109724 A127533
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), Nov 11 2004
|
|
|
Search completed in 0.002 seconds
|
