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
Keywords
Examples
113 = 81+16+16 is in the sequence.
Links
- Donovan Johnson, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A003337.
Programs
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Mathematica
Select[Prime@ Range[2^12], And[Length[#] > 0, AnyTrue[#, AllTrue[#, # > 0 &] &]] &@ PowersRepresentations[#, 3, 4] &] (* Michael De Vlieger, Aug 10 2023 *)
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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