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%I #12 Nov 06 2018 04:33:00
%S 7,19,31,37,43,61,67,73,79,97,103,109,127,139,151,157,163,181,193,199,
%T 223,241,277,349,463,601
%N Primes p == 1 (mod 3) for which A261029(26*p) = 3.
%C By theorem in A272382, case q=13, the sequence is finite with a(n) <= 676.
%H Vladimir Shevelev, <a href="http://arxiv.org/abs/1508.05748">Representation of positive integers by the form x^3+y^3+z^3-3xyz</a>, arXiv:1508.05748 [math.NT], 2015.
%t 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];
%t a29[n_] := Which[rn = r[n]; rn === False, 0, rn[[0]] === And, 1, rn[[0]] === Or, Length[rn], True, Print["error ", rn]];
%t Select[Range[1, 997, 3], PrimeQ[#] && a29[26#] == 3&] (* _Jean-François Alcover_, Nov 06 2018 *)
%Y Cf. A261029, A272381, A272382, A272384.
%K nonn,fini,full
%O 1,1
%A _Vladimir Shevelev_, Apr 29 2016
%E All terms (after first author's ones) were calculated by _Peter J. C. Moses_, Apr 29 2016
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