

A106130


Numbers k such that kth semiprime == 5 (mod k).


1



1, 60, 67, 68, 6919, 613380, 613426, 613558, 613596, 58155532, 58155539, 58155541, 58155542, 58155544
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OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..14.


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.
Sequence in context: A066722 A080862 A239415 * A216828 A131564 A036457
Adjacent sequences: A106127 A106128 A106129 * A106131 A106132 A106133


KEYWORD

nonn,hard,more


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


STATUS

approved



