A272404 Primes p == 1 (mod 3) for which A261029(26*p) = 3.

7, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 223, 241, 277, 349, 463, 601

Offset: 1

Author

Vladimir Shevelev, Apr 29 2016

Keywords

• nonn
• fini
• full

Comments

By theorem in A272382, case q=13, the sequence is finite with a(n) <= 676.

Links

• Vladimir Shevelev, Representation of positive integers by the form x^3+y^3+z^3-3xyz, arXiv:1508.05748 [math.NT], 2015.

Crossrefs

Cf. A261029, A272381, A272382, A272384.

Programs

Mathematica

r[n_] := Reduce[0 <= x <= y <= z && z >= x + 1 && n == x^3 + y^3 + z^3 - 3 x y z, {x, y, z}, Integers];
a29[n_] := Which[rn = r[n]; rn === False, 0, rn[[0]] === And, 1, rn[[0]] === Or, Length[rn], True, Print["error ", rn]];
Select[Range[1, 997, 3], PrimeQ[#] && a29[26#] == 3&] (* Jean-François Alcover, Nov 06 2018 *)

Extensions

All terms (after first author's ones) were calculated by Peter J. C. Moses, Apr 29 2016