A126657 Prime numbers that are the sum of three distinct positive fourth powers.

353, 1553, 5393, 6833, 7187, 7793, 7873, 8963, 9043, 9587, 10337, 11953, 13697, 14177, 14723, 16193, 17123, 20753, 21283, 21377, 21617, 23603, 25457, 28643, 29873, 30113, 30817, 31393, 35393, 35747, 39857, 43283, 45233, 45377, 46273

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Example

1553= 1^4 + 4^4 + 6^4 = 1 + 256 + 1296.
6833 = 2^4 + 4^4 + 9^4 = 16 + 256 + 6561.
21377 = 2^4 + 5^4 + 12^4 = 16 + 625 + 20736.
35747 = 5^4 + 9^4 + 13^4 = 625 + 6561 + 28561.

Mathematica

Union[Select[Total/@Subsets[Range[20]^4, {3}], PrimeQ]] (* Harvey P. Dale, May 08 2012 *)

Prog

(PARI) {m=15; p=m^4; v=vector(m, x, x^4); w=[]; for(i=1, m-2, for(j=i+1, m-1, for(k=j+1, m, if((n=v[i]+v[j]+v[k])<p&&isprime(n), w=concat(w, n))))); w=listsort(List(w), 1); for(j=1, #w-1, print1(w[j], ", "))} /* Klaus Brockhaus, Feb 11 2007 */

Crossrefs

Cf. A125516, A126658.

Sequence in context: A265449 A142785 A259958 * A122718 A300364 A098678

Adjacent sequences: A126654 A126655 A126656 * A126658 A126659 A126660

Keyword

nonn

Author

Tomas Xordan, Feb 09 2007

Extensions

Edited, corrected and extended by Klaus Brockhaus, Feb 11 2007

Status

approved