%I #9 Feb 26 2021 13:40:40

%S 2,6,18,24,26,30,38,56,72,90,104,120,152,158,162,174,206,218,288,294,

%T 318,342,344,350,354,360,378,408,446,458,486,510,522,534,558,690,696,

%U 698,726,776,792,824,878,894,910,936,990,992,1016,1056,1078,1098,1152,1170,1184,1256,1278,1286,1330

%N Numbers k such that both bigomega(k)+sopfr(k) and bigomega(k)+sopfr(k)+k are prime.

%C Numbers k such that A001222(k)+A001414(k) and A001222(k)+A001414(k)+k are prime.

%C All terms are even.

%C Semiprimes in the sequence are 2*p where p is in the intersection of A023200 and A023209.

%H Robert Israel, <a href="/A342035/b342035.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 24 = 2^3*3 is in the sequence because A001222(24) = 3+1 = 4, A001414(24) = 3*2+3 = 9, and 4+9 = 13 and 4+9+24 = 37 are prime.

%p filter:= proc(n) local k,v;

%p v:= add(k[2]*(1+k[1]), k = ifactors(n)[2]);

%p isprime(v) and isprime(n+v)

%p end proc:

%p select(filter, [seq(i,i=2..2000,2)]);

%Y Cf. A001222, A001414, A023200, A023209.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Feb 25 2021