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

1,2

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

Links

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

Lucas A. Brown, semiprimemods.py

Example

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

Prog

(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

Crossrefs

Cf. A001358, A357023.

Sequence in context: A066722 A080862 A239415 * A216828 A345997 A131564

Adjacent sequences: A106127 A106128 A106129 * A106131 A106132 A106133

Keyword

nonn,hard

Author

Shyam Sunder Gupta, May 07 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

Status

approved