A352132 - OEIS

%I #12 May 16 2023 10:40:09

%S 6,10,118,119,129,155,287,295,299,319,377,413,447,469,511,538,629,681,

%T 699,717,785,831,865,913,1003,1073,1077,1111,1115,1137,1141,1145,1267,

%U 1343,1345,1379,1393,1437,1469,1509,1687,1817,1835,1919,1923,1981,2167,2173,2177,2195,2245,2429,2479,2569

%N Numbers k such that k, k+4, 3*k+4 and 3*k+8 are all semiprimes.

%C Numbers k such that k and 3*k+4 are both in A175648.

%C Even terms are 2*k for k in A174920.

%H Robert Israel, <a href="/A352132/b352132.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 119 is a term because 119 = 7*17, 119+4 = 123 = 3*41, 3*119+4 = 361 = 19^2 and 3*119+8 = 365 = 5*73 are semiprimes.

%p filter:= proc(x)

%p numtheory:-bigomega(x) = 2 and numtheory:-bigomega(x+4) = 2 and numtheory:-bigomega(3*x+4) = 2 and numtheory:-bigomega(3*x+8)=2

%p end proc:

%p select(filter, [$1..3000]);

%t okQ[k_] := AllTrue[{k, k+4, 3k+4, 3k+8}, PrimeOmega[#] == 2&];

%t Select[Range[3000], okQ] (* _Jean-François Alcover_, May 16 2023 *)

%Y Cf. A001358, A174920, A175648.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Mar 05 2022