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A279393 Bisection of primes congruent to 1 modulo 4 (A002144), depending on the corresponding sum of the A002972 and 2*A002973 entries being congruent to 1 modulo 4 or not. Here we give the second case.

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%I A279393 #13 Apr 20 2025 20:13:50
%S A279393 5,29,37,61,73,101,113,137,173,181,193,197,241,269,277,293,349,389,
%T A279393 409,449,509,521,541,593,613,617,653,661,673,677,701,757,761,773,821,
%U A279393 877,929,937,941,977,1009,1033,1069,1093,1109,1117,1129,1181,1217,1237,1249,1289
%N A279393 Bisection of primes congruent to 1 modulo 4 (A002144), depending on the corresponding sum of the A002972 and 2*A002973 entries being congruent to 1 modulo 4 or not. Here we give the second case.
%C A279393 See A279392 for details of this bisection of the primes of A002144. This sequence gives the part II of primes congruent 1 modulo 4.
%F A279393 A prime A002144(m) = A(m)^2 + B(m)^2 belongs to this sequence iff (-1)^((A(m)-1)/2 + B(m)/2) = -1, where A(m) = A002972(m) and B(m)/2 = A002973(m).
%e A279393 a(1) = 5 = A002144(1) and A002972(1) = 1 and 2*A002973(1) = 2, hence 1 + 2 = 3 == 3 (mod 4), and 5 belongs to part II of this bisection.
%Y A279393 Cf. A002144, A002972, A002973, A279392.
%K A279393 nonn,easy
%O A279393 1,1
%A A279393 _Wolfdieter Lang_, Dec 11 2016
%E A279393 More terms from _Jinyuan Wang_, Apr 20 2025