cp's OEIS Frontend

A111168 Semiprimes n such that 2*n - 1 is also a semiprime.

%I A111168 #11 Jul 23 2025 13:23:28
%S A111168 25,26,33,35,39,46,58,62,65,85,93,94,111,118,119,133,134,145,146,155,
%T A111168 161,178,183,202,206,209,214,219,226,235,237,247,249,253,259,265,267,
%U A111168 287,291,295,299,334,335,341,361,362,377,382,386,391,393,395,407,422
%N A111168 Semiprimes n such that 2*n - 1 is also a semiprime.
%C A111168 Define an m-th degree Tomaszewski n-chain of the first (second) kind and length k to be a sequence of n-almost primes p(1) < p(2) < ... < p(k) such that s(i+1) = m*s(i) +(-) 1 for i = 1, ..., k-1. Notice that a 2nd degree Tomaszewski 1-chain of the first (second) kind is the familiar Cunningham chain of the first (second) kind.
%H A111168 Charles R Greathouse IV, <a href="/A111168/b111168.txt">Table of n, a(n) for n = 1..10000</a>
%F A111168 {a(n)} = a(n) is an element of A001358 and 2*a(n)-1 is an element of A001358.
%e A111168 n s(n) s*2-1
%e A111168 1 25 = 5^2 49 = 7^2
%e A111168 2 26 = 2 * 13 51 = 3 * 17
%e A111168 3 33 = 3 * 11 65 = 5 * 13
%e A111168 4 35 = 5 * 7 69 = 3 * 23
%e A111168 5 39 = 3 * 13 77 = 7 * 11
%t A111168 Select[Range[500],PrimeOmega[#]==PrimeOmega[2#-1]==2&]  (* _Harvey P. Dale_, Jul 23 2025 *)
%o A111168 (PARI) is(n)=bigomega(n)==2 && bigomega(2*n-1)==2 \\ _Charles R Greathouse IV_, Jan 31 2017
%Y A111168 Cf. A001358, A111153, A111170, A111171, A111173, A111176.
%K A111168 easy,nonn
%O A111168 1,1
%A A111168 _Jonathan Vos Post_, Oct 21 2005
%E A111168 Extended by _Ray Chandler_, Oct 22 2005