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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.
2

%I #9 May 27 2024 07:15:27

%S 5,29,37,61,73,101,113,137,173,181,193,197,241,269,277,293,349,389,

%T 409,449,509,521,541,593,613,617,653,661,673,677,701,757,761,773,821

%N 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 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 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 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 Cf. A279392, A002144, A002972, A002973.

%K nonn,easy,more

%O 1,1

%A _Wolfdieter Lang_, Dec 11 2016