A106127 Numbers k such that k-th semiprime == 2 (mod k).

1, 2, 4, 39, 51, 52, 71, 6920, 613377, 613381, 613405, 613433, 613437, 613449, 613455, 613536, 613537, 613548, 613557, 613569, 613581, 613583, 613587, 613588, 613608, 613613, 58155550, 58155570, 6384425447, 6384425465, 6384425505, 6384425531, 6384425567

Offset: 1

Author

Shyam Sunder Gupta, May 07 2005

Keywords

• hard
• nonn

Comments

No more terms through 160788536. - Ryan Propper, May 09 2006

a(34) > 10^12. - Lucas A. Brown, Oct 17 2020

Examples

			a(3)=4 is a term because the 4th semiprime (i.e., 10) == 2 (mod 4).
		

Links

• Lucas A. Brown, semiprimemods.py

Crossrefs

Cf. A001358, A356755.

Programs

Mathematica

SemiprimeQ[n_] := (Plus @@ Last /@ FactorInteger[n] == 2); i = 0; Do[If[SemiprimeQ[n], i++; If[Mod[n, i] == 2, Print[i]]], {n, 10^9}] (* Ryan Propper, May 09 2006 *)

Extensions

More terms from Ryan Propper, May 09 2006

a(1), a(2), and a(29)-a(33) from Lucas A. Brown, Oct 17 2020