A085318 Primes which are the sum of three positive 4th powers.

3, 83, 113, 163, 353, 593, 787, 1553, 2593, 3217, 4993, 5393, 6563, 6833, 7187, 7793, 7873, 8273, 8963, 9043, 9587, 10337, 11953, 13697, 14177, 14723, 14753, 16193, 17123, 20753, 21283, 21377, 21617, 23603, 25457, 26561, 27763, 28643, 28723

Offset

1,1

Links

Donovan Johnson, Table of n, a(n) for n = 1..10000

Example

113 = 81+16+16 is in the sequence.

Mathematica

Select[Prime@ Range[2^12], And[Length[#] > 0, AnyTrue[#, AllTrue[#, # > 0 &] &]] &@ PowersRepresentations[#, 3, 4] &] (* Michael De Vlieger, Aug 10 2023 *)

Prog

(PARI) lista(nn) = {v = vector(nn, i, i^4); w = vector(0); for (i=1, nn, for (j=1, nn, for (k=1, nn, w = Set(concat(w, v[i]+v[j]+v[k])); ); ); ); for (i=1, #w, if (isprime(wp=w[i]) && (wp < vecmax(v)), print1(wp, ", ")); ); } \\ Michel Marcus, Dec 19 2013

Crossrefs

Cf. A003337.

Sequence in context: A158995 A079652 A139897 * A101717 A053974 A239637

Adjacent sequences: A085315 A085316 A085317 * A085319 A085320 A085321

Keyword

nonn

Author

Labos Elemer, Jul 01 2003

Status

approved