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A180152 Numbers k such that the sum of the first k semiprimes is a prime.

%I A180152 #18 Sep 08 2022 08:45:54
%S A180152 3,4,5,7,8,15,21,22,37,56,59,62,82,85,89,91,114,119,121,129,139,146,
%T A180152 168,169,189,195,197,214,227,258,286,295,312,333,341,352,360,361,387,
%U A180152 400,419,426,434,437,440,466,470,483,495,497,504,556,595,610,619,629,636
%N A180152 Numbers k such that the sum of the first k semiprimes is a prime.
%H A180152 K. Brockhaus, <a href="/A180152/b180152.txt">Table of n, a(n) for n = 1..10000</a>
%e A180152 21 is a term because the sum of the first 21 semiprimes is 647, which is prime.
%p A180152 A062198 := proc(n) add( A001358(i),i=1..n) ; end proc:
%p A180152 isA180152 := proc(n) isprime( A062198(n)) ; end proc:
%p A180152 for n from 1 to 1000 do if isA180152(n) then printf("%d,",n) ; end if; end do: # _R. J. Mathar_, Aug 14 2010
%t A180152 Position[Accumulate[Select[Range[10000],PrimeOmega[#]==2&]],_?PrimeQ] // Flatten (* _Harvey P. Dale_, Feb 17 2021 *)
%o A180152 (Magma) SP:=[ n: n in [2..3000] | &+[ k[2]: k in Factorization(n) ] eq 2 ]; V:=[]; s:=0; for j in [1..640] do s+:=SP[j]; if IsPrime(s) then Append(~V, j); end if; end for; V; // _Klaus Brockhaus_, Aug 14 2010
%Y A180152 Cf. A062198, A000040.
%K A180152 nonn
%O A180152 1,1
%A A180152 _Jason G. Wurtzel_, Aug 13 2010
%E A180152 More terms from _Klaus Brockhaus_ and _R. J. Mathar_, Aug 14 2010