cp's OEIS Frontend

A368670 Numbers k such that k, k + 1, k + 2, and k + 4 are all semiprimes.

%I A368670 #9 Jan 07 2024 12:16:09
%S A368670 141,201,213,217,301,1137,1345,1401,1761,1837,1893,1941,1981,2101,
%T A368670 3097,3865,3957,4413,4533,4881,5997,6157,6241,7113,7141,7165,7401,
%U A368670 7977,8185,8257,8913,9753,9985,10117,11013,11181,11377,11757,12057,13953,14037,14253,14917,14977,14997,16177,16293,16437,16593
%N A368670 Numbers k such that k, k + 1, k + 2, and k + 4 are all semiprimes.
%C A368670 k, k + 1, k + 2 and k + 3 can't all be semiprimes, as one of them is divisible by 4.
%C A368670 All terms == 1 (mod 4).
%H A368670 Robert Israel, <a href="/A368670/b368670.txt">Table of n, a(n) for n = 1..10000</a>
%e A368670 a(3) = 213 is a term because 213 = 3 * 71, 214 = 2 * 107, 215 = 5 * 43 and 217 = 7 * 31 are all semiprimes.
%p A368670 select(t -> numtheory:-bigomega(t)=2 and numtheory:-bigomega(t+1)=2 and numtheory:-bigomega(t+2)=2 and numtheory:-bigomega(t+4)=2, 4 * [$1..10000] +~ 1);
%t A368670 Select[Range[17000], PrimeOmega[#] == PrimeOmega[#+1] == PrimeOmega[#+2] == PrimeOmega[#+4] == 2 &] (* _Stefano Spezia_, Jan 02 2024 *)
%Y A368670 Cf. A001358, A056809, A070552.
%K A368670 nonn
%O A368670 1,1
%A A368670 _Robert Israel_, Jan 02 2024