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A189072 Semiprimes in A007504 (the sum of first n primes).

%I A189072 #15 Dec 22 2018 12:21:22
%S A189072 10,58,77,129,381,501,791,1371,1851,2127,2427,2747,3831,4227,4661,
%T A189072 6081,6338,7141,7418,9206,9523,11599,12718,15537,20059,20546,21037,
%U A189072 26369,27517,29897,34915,36227,45434,47721,48494,49281,50887,51698,52519,54169,57547
%N A189072 Semiprimes in A007504 (the sum of first n primes).
%C A189072 a(n) = A007504(k(n)), values of k(n) = 3, 7, 8, 10, 16, 18, 22, 28, 32, 34, 36, 38, 44, 46, 48, 54, 55, 58, 59, 65, 66, 72, 75, 82, 92, 93, 94, 104, 106, 110, 118, 120, 133, 136, 137, 138, 140, 141, 142, 144, 148, 150, 154, 156, 164, 168, 170, 174, 190, 194, 202, 210, 212, 218, 224, 226, 232, 234, 236, 244, 246, 249, 250, 256, 264, 272, 276, 277, 286, 294, 298, 300.
%C A189072 Intersection of A007504 and A001358. - _Robert Israel_, Jun 23 2017
%H A189072 Robert Israel, <a href="/A189072/b189072.txt">Table of n, a(n) for n = 1..10000</a>
%e A189072 10 = 2*5 = A007504(3), 58 = 2*29 = A007504(7), 77 = 7*11 = A007504(8).
%p A189072 PS:= ListTools:-PartialSums(select(isprime, [2,seq(i,i=3..10^4,2)])):
%p A189072 select(numtheory:-bigomega = 2, PS); # _Robert Israel_, Jun 23 2017
%t A189072 semiPrimeQ[n_Integer] := Total[FactorInteger[n]][[2]] == 2; Select[Accumulate[Prime[Range[100]]], semiPrimeQ] (* _T. D. Noe_, Apr 20 2011 *)
%t A189072 With[{nn=200},Select[Accumulate[Prime[Range[nn]]],PrimeOmega[#]==2&]] (* _Harvey P. Dale_, Dec 22 2018 *)
%o A189072 (PARI) {a=0;s=[];forprime(p=2,10^4,2==bigomega(a=a+p)&s=concat(s,a));s}
%Y A189072 Cf. A013918 (primes in A007504).
%Y A189072 Cf. A007504, A001358.
%K A189072 nonn
%O A189072 1,1
%A A189072 _Zak Seidov_, Apr 16 2011