A272205 A bisection of the primes congruent to 1 modulo 3 (A002476). This is the part depending on the corresponding A001479 entry being congruent to 4 or 5 modulo 6.

19, 37, 43, 73, 103, 127, 163, 229, 283, 313, 331, 337, 379, 397, 421, 457, 463, 487, 499, 523, 541, 577, 607, 613, 619, 631, 691, 709, 727, 787, 811, 829, 853, 859, 877, 883, 967, 991, 997

Offset

1,1

Comments

The other part of this bisection appears in A272204.

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. The present sequence gives such primes corresponding to A(m) == 4, 5 (mod 6). The ones corresponding to A(m) == 1, 2 (mod 6) (the complement) are given in A272205.

The corresponding A001479 entries are 4, 5, 4, 5, 10, 10, 4, 11, 16, 11, 16, 17, 4, 17, 11, 5, 10, 22, 16, 4, 23, 23, 10, 5, 16, 22, 4, 11, 22, 28, 28, 23, 29, 28, 17, 4, 10, 22, 5, ...

See A272204 for a comment on the relevance of this bisection in connection with the signs of the q-expansion coefficients of the modular cusp form eta^{12}(12*z) / (eta^4(6*z)*eta^4(24*z)).

Links

Table of n, a(n) for n=1..39.

Formula

This sequence collects the 1 (mod 3) primes p(m) = A002476(m) = A(m)^2 + 3*B(m)^2 with positive A(m) == 4, 5 (mod 6), for m >= 1. A(m) = A001479(m+1).

Crossrefs

Cf. A001479, A001480, A002476, A047239, A187076, A272203, A272204 (complement relative to A002476).

Sequence in context: A134196 A217045 A139313 * A347371 A332756 A245363

Adjacent sequences: A272202 A272203 A272204 * A272206 A272207 A272208

Keyword

nonn,easy

Author

Wolfdieter Lang, May 05 2016

Status

approved