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A111171 Semiprimes S such that 3*S - 1 is also a semiprime.

%I A111171 #10 Jun 20 2018 14:18:04
%S A111171 9,21,22,25,26,49,62,65,69,74,85,93,121,122,129,133,141,146,158,161,
%T A111171 166,178,185,194,205,209,221,249,253,262,265,289,298,302,305,309,346,
%U A111171 358,361,365,381,382,386,413,446,466,473,485,489,493,501,505,514,526,553
%N A111171 Semiprimes S such that 3*S - 1 is also a semiprime.
%C A111171 This is analogous to Sophie Germain semiprimes A111153 and the chains shown are analogous to Cunningham chains of the second kind and Tomaszewski chains of the second kind. Define a 3n-1 semiprime chain of length k. This is a sequence of semiprimes s(1) < s(2) < ... < s(k) such that s(i+1) = 3*s(i) - 1 for i = 1, ..., k-1. Length 3: 9, 26, 77; 49, 146, 437; 65, 194, 581; 129, 386, 1157; 158, 473, 1418; 187, 562, 1685. Length 4: 74, 221, 662, 1985; 122, 365, 1094, 3281. Length 5: 21, 62, 185, 554, 1661.
%H A111171 Harvey P. Dale, <a href="/A111171/b111171.txt">Table of n, a(n) for n = 1..1000</a>
%F A111171 {a(n)} = a(n) is an element of A001358 and 3*a(n)-1 is an element of A001358.
%e A111171 n s(n) 3 *s -1
%e A111171 1 9 = 3^2 26 = 2 * 13
%e A111171 2 21 = 3 * 7 62 = 2 * 31
%e A111171 3 22 = 2 * 11 65 = 5 * 13
%e A111171 4 25 = 5^2 74 = 2 * 37
%e A111171 5 26 = 2 * 13 77 = 7 * 11
%e A111171 6 49 = 7^2 146 = 2 * 73
%t A111171 Select[Range[600],PrimeOmega[#]==PrimeOmega[3#-1]==2&] (* _Harvey P. Dale_, Jun 20 2018 *)
%Y A111171 Cf. A001358, A111153, A111168, A111170, A111173, A111176.
%K A111171 easy,nonn
%O A111171 1,1
%A A111171 _Jonathan Vos Post_, Oct 21 2005
%E A111171 Corrected and extended by _Ray Chandler_, Oct 22 2005