A126658 Prime numbers that are the sum of three distinct positive eighth powers.

72353, 1745153, 7444673, 44726593, 49202147, 61503553, 100006817, 100072097, 101686177, 107444417, 143046977, 214756067, 257412163, 430372577, 431661313, 435812033, 447149537, 452523713, 489805633, 530372321, 744340577, 834187553

Offset

1,1

Comments

These are also the sum of three squares and the sum of three fourth powers: 7444673 = 16^2 + 1296^2 + 2401^2 = 4^4 + 36^4 + 49^4 = 256 + 1679616 + 5764801.

Links

Table of n, a(n) for n=1..22.

Example

72353 = 2^8 + 3^8 + 4^8 = 256 + 6561 + 65536.
7444673 = 2^8 + 6^8 + 7^8 = 256 + 1679616 + 5764801.
49202147 = 5^8 + 7^8 + 9^8 = 390625 + 5764801 + 43046721.

Prog

(PARI) {m=14; p=m^8; v=vector(m, x, x^8); 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, A126657.

Sequence in context: A257206 A229322 A269320 * A251340 A183788 A369238

Adjacent sequences: A126655 A126656 A126657 * A126659 A126660 A126661

Keyword

nonn

Author

Tomas Xordan, Feb 09 2007

Extensions

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

Status

approved