A381465 Semiprimes k such that 6*k + 1 is also a semiprime.

4, 9, 14, 15, 22, 34, 39, 49, 65, 69, 74, 82, 85, 86, 93, 94, 111, 133, 145, 158, 159, 183, 185, 194, 201, 203, 209, 214, 219, 226, 235, 259, 265, 267, 289, 299, 301, 303, 319, 321, 323, 326, 327, 334, 341, 346, 358, 361, 362, 365, 371, 377, 386, 393, 403, 407, 413, 415, 422, 427, 437, 469, 471

Offset: 1

Author

Zak Seidov and Robert Israel, Feb 24 2025

Keywords

• nonn

Examples

			a(3) = 14 is a term because 14 = 2 * 7 is a semiprime and 6 * 14 + 1 = 85 = 5 * 17 is also a semiprime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A007693, A111153, A111170.

Programs

Maple

select(t -> numtheory:-bigomega(t) = 2 and numtheory:-bigomega(6*t+1)=2, [$4..1000]);

Mathematica

s = {}; Do[If[{2, 2} == PrimeOmega[{k, 6*k + 1}], AppendTo[s, k]], {k, 1000}] ; s

PARI

isok(k) = (bigomega(k)==2) && (bigomega(6*k+1)==2); \\ Michel Marcus, Feb 26 2025