cp's OEIS Frontend

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

%I A106130 #43 Oct 16 2022 12:36:59
%S A106130 1,60,67,68,6919,613380,613426,613558,613596,58155532,58155539,
%T A106130 58155541,58155542,58155544,6384425448,6384425451,6384425502,
%U A106130 6384425508,6384425516,6384425552,6384425568,6384425636,6384425646
%N A106130 Numbers k such that k-th semiprime == 5 (mod k).
%C A106130 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
%C A106130 a(32) > 10^12. - _Lucas A. Brown_, Oct 18 2020
%H A106130 Lucas A. Brown, <a href="/A106130/b106130.txt">Table of n, a(n) for n = 1..31</a>
%H A106130 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/semiprimemods.py">semiprimemods.py</a>
%e A106130 60 is a term because the 60th semiprime (i.e., 185) == 5 (mod 60).
%o A106130 (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
%Y A106130 Cf. A001358, A357023.
%K A106130 nonn,hard
%O A106130 1,2
%A A106130 _Shyam Sunder Gupta_, May 07 2005
%E A106130 More terms from _Stefan Steinerberger_, Nov 10 2005
%E A106130 a(9)-a(13) from _Donovan Johnson_, Oct 29 2008
%E A106130 Initial 1 added by _Robert Israel_, Dec 19 2017
%E A106130 a(15)-a(23) by _Lucas A. Brown_, Oct 18 2020