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A106130
Numbers k such that k-th semiprime == 5 (mod k).
3
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, 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
Sequence in context: A066722 A080862 A239415 * A216828 A345997 A131564
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