A272407 Primes p == 1 (mod 3) for which A261029(38*p) = 3.

7, 13, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397, 409, 433, 463, 499, 523, 541, 577, 601, 607, 619, 661, 757, 853, 937, 1123, 1129

Offset: 1

Author

Vladimir Shevelev, Apr 29 2016

Keywords

• nonn
• fini
• full

Comments

By theorem in A272382, case q=19, the sequence is finite with a(n)<1444.

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, A272404, A272406.

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];
a261029[n_] := Which[rn = r[n]; rn === False, 0, rn[[0]] === And, 1, rn[[0]] === Or, Length[rn], True, Print["error ", rn]];
Select[Select[Range[1, 1171, 3], PrimeQ], a261029[38 #] == 3&] (* Jean-François Alcover, Dec 04 2018 *)

Extensions

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