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

4, 14, 8567, 16499, 151211, 344891, 418831, 585197, 1049882, 1186582, 1671029, 2503966, 2989387, 4802311, 8291795, 9769711, 11420129, 13279957, 13677063, 15356513, 16258813, 24318863, 26874293, 39317497, 42862751

Offset

1,1

Comments

If we call the semiprime numbers A001358 level 1, and A092190 level 2, then this sequence is level 3.

Links

Wilmer Emiro Castrillon Calderon, Table of n, a(n) for n = 1..100

Example

a(2) = 14 = Sum_{i=1..2} A092190(i).
a(3) = 8567 = Sum_{i=1..13} A092190(i).

Mathematica

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 *)

Prog

(C++) typedef unsigned long long int ulli;
void Level3(){  vector<ulli>::iterator low;  ulli acum = 0;
    for(int i = 0; i < level2.size(); i++){
        acum += level2[i];
        low=lower_bound (semiprimes.begin(), semiprimes.end(), acum);
        if(semiprimes[low - semiprimes.begin()] == acum){
            printf("%llu\n", acum);
} } } //where level2 is a vector with A092190.

Crossrefs

Cf. A001358, A092190.

Sequence in context: A022508 A161741 A186509 * A097548 A218047 A344938

Adjacent sequences: A323082 A323083 A323084 * A323086 A323087 A323088

Keyword

nonn

Author

Wilmer Emiro Castrillon Calderon, Jan 03 2019

Status

approved