A283597 - OEIS

%I #24 Dec 23 2024 21:57:35

%S 8,14,19,41,42,43,48,49,59,74,84,85,88,92,93,97,108,113,116,132,139,

%T 144,148,149,157,158,159,162,163,189,190,193,198,209,210,211,222,223,

%U 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

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

%C Both n and n+1 are terms in A112775.

%H Robert Israel, <a href="/A283597/b283597.txt">Table of n, a(n) for n = 1..10000</a>

%p filter:= n -> numtheory:-bigomega(6*n+1) = 2 and numtheory:-bigomega(6*n+7) = 2:

%p select(filter, [$1..1000]); # _Robert Israel_, Dec 23 2024

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

%o (PARI) for(n=1, 388, if(bigomega(6*n + 1) == 2 && bigomega(6*n + 7) == 2, print1(n,", "))) \\ _Indranil Ghosh_, Mar 15 2017

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

%K nonn

%O 1,1

%A _Zak Seidov_, Mar 14 2017