A283597 Numbers n such that both 6n+1 and 6n+7 are semiprimes.

8, 14, 19, 41, 42, 43, 48, 49, 59, 74, 84, 85, 88, 92, 93, 97, 108, 113, 116, 132, 139, 144, 148, 149, 157, 158, 159, 162, 163, 189, 190, 193, 198, 209, 210, 211, 222, 223, 224, 225, 226, 227, 231, 234, 235, 250, 251, 259, 264, 272, 280, 285, 306, 307, 315, 316, 317, 318, 319, 320, 323, 326, 327, 340, 345, 349, 358, 361, 368, 376, 386, 387, 388

Offset: 1

Author

Zak Seidov, Mar 14 2017

Keywords

• nonn

Comments

Both n and n+1 are terms in A112775.

Links

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

Crossrefs

Cf. A112771 (6n+1 semiprimes), A112775 (6n+1 is semiprime), A001358 (semiprimes).

Programs

Maple

filter:= n -> numtheory:-bigomega(6*n+1) = 2 and numtheory:-bigomega(6*n+7) = 2:
select(filter, [$1..1000]); # Robert Israel, Dec 23 2024

Mathematica

po[x_]=PrimeOmega[x]; Select[Range[500], po[6# + 1] == po[6# + 7] == 2 &]

PARI

for(n=1, 388, if(bigomega(6*n + 1) == 2 && bigomega(6*n + 7) == 2, print1(n,", "))) \\ Indranil Ghosh, Mar 15 2017