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

Author

Roger L. Bagula, Sep 15 2006

Keywords

• nonn

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

Crossrefs

Cf. A000931, A001358, A053409, A100891.

Programs

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]}]]

Extensions

More terms from Alois P. Heinz, Aug 31 2017