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%I A272205 #7 May 10 2016 16:25:52
%S A272205 19,37,43,73,103,127,163,229,283,313,331,337,379,397,421,457,463,487,
%T A272205 499,523,541,577,607,613,619,631,691,709,727,787,811,829,853,859,877,
%U A272205 883,967,991,997
%N A272205 A bisection of the primes congruent to 1 modulo 3 (A002476). This is the part depending on the corresponding A001479 entry being congruent to 4 or 5 modulo 6.
%C A272205 The other part of this bisection appears in A272204.
%C A272205 Each prime == 1 (mod 3) has a unique representation A002476(m) = A(m)^2 + 3*B(m)^2 with positive A(m) = A001479(m+1) and B(m) = A001480(m+1), m >= 1. The present sequence gives such primes corresponding to A(m) == 4, 5 (mod 6). The ones corresponding to A(m) == 1, 2 (mod 6) (the complement) are given in A272205.
%C A272205 The corresponding A001479 entries are 4, 5, 4, 5, 10, 10, 4, 11, 16, 11, 16, 17, 4, 17, 11, 5, 10, 22, 16, 4, 23, 23, 10, 5, 16, 22, 4, 11, 22, 28, 28, 23, 29, 28, 17, 4, 10, 22, 5, ...
%C A272205 See  A272204 for a comment on the relevance of this bisection in connection with the signs of the q-expansion coefficients of the modular cusp form eta^{12}(12*z) / (eta^4(6*z)*eta^4(24*z)).
%F A272205 This sequence collects the 1 (mod 3) primes p(m) = A002476(m) = A(m)^2 + 3*B(m)^2 with positive A(m) == 4, 5 (mod 6), for m >= 1. A(m) = A001479(m+1).
%Y A272205 Cf. A001479, A001480, A002476, A047239, A187076, A272203, A272204 (complement relative to A002476).
%K A272205 nonn,easy
%O A272205 1,1
%A A272205 _Wolfdieter Lang_, May 05 2016

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