%I #10 Apr 21 2020 09:13:51

%S 7,31,37,67,73,79,139,151,199,211,223,229,271,307,313,337,367,397,421,

%T 439,457,541,547,571,577,613,643,709,739,751,823,829,853,877,907,919,

%U 997

%N Bisection of primes congruent to 1 modulo 3 (A002476), depending on the corresponding A001479 entry being congruent to 1 modulo 3 or not. Here the second case.

%C The other primes congruent to 1 modulo 3 are given in A272200, where also more details are given.

%C 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 (see also A001479). The present sequence gives these primes corresponding to A(m+1) not congruent 1 modulo 3. The ones corresponding to A(m+1) == 1 (mod 3) (the complement) are given in A272200.

%H Robert Israel, <a href="/A272201/b272201.txt">Table of n, a(n) for n = 1..10000</a>

%F This sequence collects the 1 (mod 3) primes p(m) = A002476(m) = A(m)^2 + 3*B(m)^2 with positive A(m) not == 1 (mod 3), for m >= 1. A(m) = A001479(m+1).

%p filter:= proc(n) local S,x,y;

%p if not isprime(n) then return false fi;

%p S:= remove(hastype,[isolve(x^2+3*y^2=n)],negative);

%p subs(S[1],x) mod 3 <> 1

%p end proc:

%p select(filter, [seq(i,i=7..1000,6)]); # _Robert Israel_, Apr 29 2019

%t filterQ[n_] := Module[{S, x, y}, If[!PrimeQ[n], Return[False]]; S = Solve[x > 0 && y > 0 && x^2 + 3 y^2 == n, Integers]; Mod[x /. S[[1]], 3] != 1];

%t Select[Range[7, 1000, 6], filterQ] (* _Jean-François Alcover_, Apr 21 2020, after _Robert Israel_ *)

%Y Cf. A000727, A001479, A002476, A001480, A272198, A272200 (complement relative to A002476).

%K nonn,easy

%O 1,1

%A _Wolfdieter Lang_, Apr 28 2016