A106130 Numbers k such that k-th semiprime == 5 (mod k).

1, 60, 67, 68, 6919, 613380, 613426, 613558, 613596, 58155532, 58155539, 58155541, 58155542, 58155544, 6384425448, 6384425451, 6384425502, 6384425508, 6384425516, 6384425552, 6384425568, 6384425636, 6384425646

Offset: 1

Author

Shyam Sunder Gupta, May 07 2005

Keywords

• nonn
• hard

Comments

The terms 60, 67, and 68 are numbers k such that the k-th semiprime is 3k+5; at k=6919, the k-th semiprime is 4k+5; at k = 613380, 613426, 613558, and 613596, the k-th semiprime is 5k+5; and at k = 58155532, 58155539, 58155541, 58155542, and 58155544, the k-th semiprime is 6k+5. No more terms should be expected up to through at least k = 6*10^9, where the ratio (k-th semiprime)/k is approaching 7. - Jon E. Schoenfield, Dec 17 2017

a(32) > 10^12. - Lucas A. Brown, Oct 18 2020

Examples

			60 is a term because the 60th semiprime (i.e., 185) == 5 (mod 60).
		

Links

• Lucas A. Brown, Table of n, a(n) for n = 1..31
• Lucas A. Brown, semiprimemods.py

Crossrefs

Cf. A001358, A357023.

Programs

MuPAD

order := 0; for n from 1 to 10^100 do if numlib::Omega(n) = 2 then order := order+1; if n mod order = 5 then print(order);end_if;end_if;end_for; // Stefan Steinerberger, Nov 10 2005

Extensions

More terms from Stefan Steinerberger, Nov 10 2005

a(9)-a(13) from Donovan Johnson, Oct 29 2008

Initial 1 added by Robert Israel, Dec 19 2017

a(15)-a(23) by Lucas A. Brown, Oct 18 2020