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.

5, 29, 37, 61, 73, 101, 113, 137, 173, 181, 193, 197, 241, 269, 277, 293, 349, 389, 409, 449, 509, 521, 541, 593, 613, 617, 653, 661, 673, 677, 701, 757, 761, 773, 821, 877, 929, 937, 941, 977, 1009, 1033, 1069, 1093, 1109, 1117, 1129, 1181, 1217, 1237, 1249, 1289

Offset: 1

Author

Wolfdieter Lang, Dec 11 2016

Keywords

• nonn
• easy

Comments

See A279392 for details of this bisection of the primes of A002144. This sequence gives the part II of primes congruent 1 modulo 4.

Examples

			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.
		

Crossrefs

Cf. A002144, A002972, A002973, A279392.

Formula

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).

Extensions

More terms from Jinyuan Wang, Apr 20 2025