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A323085 Semiprimes that are the sum of the first k terms of A092190 for some k.

%I A323085 #17 Jan 28 2019 13:57:43
%S A323085 4,14,8567,16499,151211,344891,418831,585197,1049882,1186582,1671029,
%T A323085 2503966,2989387,4802311,8291795,9769711,11420129,13279957,13677063,
%U A323085 15356513,16258813,24318863,26874293,39317497,42862751
%N A323085 Semiprimes that are the sum of the first k terms of A092190 for some k.
%C A323085 If we call the semiprime numbers A001358 level 1, and A092190 level 2, then this sequence is level 3.
%H A323085 Wilmer Emiro Castrillon Calderon, <a href="/A323085/b323085.txt">Table of n, a(n) for n = 1..100</a>
%e A323085 a(2) = 14 = Sum_{i=1..2} A092190(i).
%e A323085 a(3) = 8567 = Sum_{i=1..13} A092190(i).
%t A323085 f[w_] := Select[Most@ NestWhile[Append[#1, {#2, #2 + #1[[-1, -1]]}] & @@ {#, w[[Length@ # + 1]]} &, {{#, #}} &@ First[w], #[[-1, -1]] <= Max@ w &][[All, -1]], PrimeOmega@ # == 2 &]; Block[{s = Select[Range[10^6], PrimeOmega@ # == 2 &], t}, f@ f@ s] (* _Michael De Vlieger_, Jan 04 2019 *)
%o A323085 (C++) typedef unsigned long long int ulli;
%o A323085 void Level3(){  vector<ulli>::iterator low;  ulli acum = 0;
%o A323085     for(int i = 0; i < level2.size(); i++){
%o A323085         acum += level2[i];
%o A323085         low=lower_bound (semiprimes.begin(), semiprimes.end(), acum);
%o A323085         if(semiprimes[low - semiprimes.begin()] == acum){
%o A323085             printf("%llu\n", acum);
%o A323085 } } } //where level2 is a vector with A092190.
%Y A323085 Cf. A001358, A092190.
%K A323085 nonn
%O A323085 1,1
%A A323085 _Wilmer Emiro Castrillon Calderon_, Jan 03 2019