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Primes p == 1 (mod 3) for which A261029(46*p) = 2.
4

%I #8 Dec 06 2018 14:50:50

%S 7,13,19,31,37,43,61,67,73,79,97,103,109,127,139,151,157,163,181,193,

%T 199,211,223,229,241,271,277,283,307,313,331,337,349,367,373,379,397,

%U 409,421,433,439,457,463,487,499,523,541,547,571,577,613,631,643,673,709,733,739,787,811,829,859,877,907,1009,1063,1093,1117,1279,1297,1381,1483,1489,1723

%N Primes p == 1 (mod 3) for which A261029(46*p) = 2.

%C By theorem in A272384, case q=23, the sequence is finite with a(n)<2116.

%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[Select[Range[1, 2002, 3], PrimeQ], a29[ 46 # ] == 2&] (* _Jean-François Alcover_, Dec 06 2018 *)

%Y Cf. A261029, A272381, A272382, A272384, A272404, A272406, A272407.

%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