This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A272382 #18 Nov 21 2018 09:23:12
%S A272382 13,19,31,37,43,61,67,97,157
%N A272382 Primes p == 1 (mod 3) for which A261029(14*p) = 3.
%C A272382 _Peter J. C. Moses_ did not find any term > 157. The author proved that the sequence is full. Moreover, he proved the following more general result.
%C A272382 Theorem. If p,q == 1 (mod 3) are prime and A261029(2*q*p) > 2, then sqrt(q)/2 < p < 4*q^2.
%C A272382 In this sequence q=7, so a(n) < 196.
%C A272382 Proof of Theorem is similar to proof of the theorem in A272384.
%H A272382 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 A272382 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 A272382 a29[n_] := Which[rn = r[n]; rn === False, 0, rn[[0]] === And, 1, rn[[0]] === Or, Length[rn], True, Print["error ", rn]];
%t A272382 Select[Select[Range[1, 1000, 3], PrimeQ], a29[14 #] == 3&] (* _Jean-François Alcover_, Nov 21 2018 *)
%Y A272382 Cf. A261029, A272381, A272384, A272404, A272406, A272407, A272409.
%K A272382 nonn,fini,full
%O A272382 1,1
%A A272382 _Vladimir Shevelev_, Apr 28 2016