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%I A342035 #9 Feb 26 2021 13:40:40
%S A342035 2,6,18,24,26,30,38,56,72,90,104,120,152,158,162,174,206,218,288,294,
%T A342035 318,342,344,350,354,360,378,408,446,458,486,510,522,534,558,690,696,
%U A342035 698,726,776,792,824,878,894,910,936,990,992,1016,1056,1078,1098,1152,1170,1184,1256,1278,1286,1330
%N A342035 Numbers k such that both bigomega(k)+sopfr(k) and bigomega(k)+sopfr(k)+k are prime.
%C A342035 Numbers k such that A001222(k)+A001414(k) and A001222(k)+A001414(k)+k are prime.
%C A342035 All terms are even.
%C A342035 Semiprimes in the sequence are 2*p where p is in the intersection of A023200 and A023209.
%H A342035 Robert Israel, <a href="/A342035/b342035.txt">Table of n, a(n) for n = 1..10000</a>
%e A342035 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 A342035 filter:= proc(n) local k,v;
%p A342035   v:= add(k[2]*(1+k[1]), k = ifactors(n)[2]);
%p A342035   isprime(v) and isprime(n+v)
%p A342035 end proc:
%p A342035 select(filter, [seq(i,i=2..2000,2)]);
%Y A342035 Cf. A001222, A001414, A023200, A023209.
%K A342035 nonn
%O A342035 1,1
%A A342035 _J. M. Bergot_ and _Robert Israel_, Feb 25 2021

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