A106131 Numbers k such that the k-th semiprime == 6 (mod k).

1, 2, 3, 4, 8, 10, 57, 59, 69, 6914, 613376, 613403, 613431, 613432, 613436, 613447, 613453, 613483, 613484, 613507, 613511, 613513, 613516, 613531, 613535, 613541, 613547, 613579, 613580, 613597, 613607, 6384425453, 6384425504, 6384425519, 6384425555

Offset: 1

Author

Shyam Sunder Gupta, May 07 2005

Keywords

• hard
• nonn

Comments

a(42) > 10^12. - Lucas A. Brown, Oct 19 2020

Examples

			a(5) = 8 is a term because the 8th semiprime is 22 and 22 == 6 (mod 8).
		

Links

• Lucas A. Brown, Table of n, a(n) for n = 1..41
• Lucas A. Brown, semiprimemods.py

Crossrefs

Cf. A001358, A356135.

Programs

Mathematica

Module[{sp=Select[Range[10^7],PrimeOmega[#]==2&]},Flatten[ Position[ Thread[ {sp, Range[ Length[sp]]}],?(Mod[#[[1]],#[[2]]]==6&),{1}, Heads-> False]]] (* _Harvey P. Dale, May 09 2015 *)

Extensions

a(1)-a(4) and a(32)-a(41) by Lucas A. Brown, Oct 19 2020