A369105 Primes p such that p+2 has only prime factors congruent to -1 modulo 4.

5, 7, 17, 19, 29, 31, 41, 47, 61, 67, 79, 97, 101, 127, 131, 137, 139, 149, 197, 199, 211, 229, 241, 251, 269, 277, 281, 307, 359, 379, 397, 421, 439, 461, 467, 487, 499, 521, 569, 571, 587, 601, 617, 619, 631, 641, 647, 691, 709, 719, 727, 751, 757, 787, 809, 811

Offset

1,1

Comments

Jones and Zvonkin call these primes BCC primes, where BCC stands for Bujalance, Cirre, and Conder.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

E. Bujalance, F. J. Cirre, and M. D. E. Conder, Bounds on the orders of groups of automorphisms of a pseudo-real surface of given genus, Journal of the London Mathematical Society, Volume 101, Issue 2, p. 877-906, (2019).

Gareth A. Jones and Alexander K. Zvonkin, A number-theoretic problem concerning pseudo-real Riemann surfaces, arXiv:2401.00270 [math.NT], 2023. See page 1.

Mathematica

Select[Prime[Range[150]], PrimeQ[f=First/@FactorInteger[#+2]] == Table[True, {j, PrimeNu[#+2]}] && Mod[f, 4] == Table[3, {m, PrimeNu[#+2]}] &]

Prog

(PARI) is1(n) = {my(p = factor(n)[, 1]); for(i = 1, #p, if(p[i] % 4 == 1, return(0))); 1; };
lista(pmax) = forprime(p = 3, pmax, if(is1(p+2), print1(p, ", "))); \\ Amiram Eldar, Jun 03 2024

Crossrefs

Cf. A001221, A004614, A004767, A027748, A369107, A369108, A369109, A369111.

Sequence in context: A092242 A003630 A122565 * A247607 A079016 A106120

Adjacent sequences: A369102 A369103 A369104 * A369106 A369107 A369108

Keyword

nonn

Author

Stefano Spezia, Jan 13 2024

Status

approved