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

1,1

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.

Links

Table of n, a(n) for n=1..52.

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).

Example

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.

Sequence in context: A053244 A096696 A115279 * A182288 A087879 A091729

Adjacent sequences: A279390 A279391 A279392 * A279394 A279395 A279396

Keyword

nonn,easy

Author

Wolfdieter Lang, Dec 11 2016

Extensions

More terms from Jinyuan Wang, Apr 20 2025

Status

approved