A365939 Gilbreath transform of semiprimes (A001358).
4, 2, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1
Offset: 1
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Mathematica
A365939list[upto_]:=If[upto<4,{},Module[{d=Select[Range[upto],PrimeOmega[#]==2&]},Join[{4},Table[First[d=Abs[Differences[d]]],Length[d]-1]]]];A365939list[500] (* Paolo Xausa, Sep 25 2023 *)
Extensions
More terms from Pontus von Brömssen, Sep 25 2023