A122498 Padovan numbers that are semiprimes.

4, 9, 21, 49, 65, 86, 265, 1081, 1897, 2513, 7739, 97229, 128801, 299426, 922111, 1221537, 2839729, 62608681, 338356945, 53406819691, 2066337330754, 6363483400447, 8429820731201, 432062194544201, 7190854504969591, 12619069972000553, 16716708595637087

Offset

1,1

Comments

The smallest candidate for the next term in the b-file is A000931(1958), which is composite with 239 digits and an unknown number of prime factors. - Hugo Pfoertner, Sep 07 2017

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..54

Eric Weisstein's World of Mathematics, Semiprime

Maple

select(x-> numtheory[bigomega](x)=2, [(<<0|1|0>,
   <0|0|1>, <1|1|0>>^i)[1$2]$i=0..300])[];  # Alois P. Heinz, Aug 31 2017

Mathematica

SemiprimeQ[1] := False SemiprimeQ[n_Integer] := Plus @@ (Last /@ FactorInteger[n]) == 2 a = Table[ SeriesCoefficient[ Series[x/(1 - x^2 - x^3), {x, 0, 50}], n], {n, 0, 50}] f[n_] = If[SemiprimeQ[a[[n]]] == True, a[[n]], {}] Flatten[Table[f[n], {n, 1, Length[a]}]]

Crossrefs

Cf. A000931, A001358, A053409, A100891.

Sequence in context: A348407 A103040 A084861 * A132750 A297296 A048582

Adjacent sequences: A122495 A122496 A122497 * A122499 A122500 A122501

Keyword

nonn

Author

Roger L. Bagula, Sep 15 2006

Extensions

More terms from Alois P. Heinz, Aug 31 2017

Status

approved