A350704 Composite numbers that have no Sophie Germain prime factors.

49, 91, 119, 133, 169, 217, 221, 247, 259, 289, 301, 323, 329, 343, 361, 403, 413, 427, 469, 481, 497, 511, 527, 553, 559, 589, 611, 629, 637, 679, 703, 707, 721, 731, 749, 763, 767, 793, 799, 817, 833, 871, 889, 893, 923, 931, 949, 959, 961, 973, 1003, 1027, 1037, 1043

Offset

1,1

Comments

A157342 is a subsequence. First differs at a(14) = 343.

A350705 is a subsequence too.

Links

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Example

a(2) = 91 = 7 * 13 and {7, 13} are not in A005384.

Mathematica

Select[Range[1000], CompositeQ[#] && AllTrue[FactorInteger[#][[;; , 1]], !PrimeQ[2*#1 + 1] &] &] (* Amiram Eldar, Feb 12 2022 *)

Prog

(Python)
from sympy import primefactors, isprime
print([n for n in range(2, 1044) if not isprime(n) and all(not isprime(p*2+1) for p in primefactors(n))])
(PARI) isok(m) = if ((m>1) && !isprime(m), !#select(x->isprime(2*x+1), factor(m)[, 1])); \\ Michel Marcus, Feb 11 2022

Crossrefs

Cf. A157342, A005384, A053176, A350705, A350706.

Sequence in context: A231275 A158725 A090825 * A157342 A230226 A178705

Adjacent sequences: A350701 A350702 A350703 * A350705 A350706 A350707

Keyword

nonn

Author

Karl-Heinz Hofmann, Feb 11 2022

Status

approved