A111168 - OEIS

%I #9 Jan 31 2017 15:42:11

%S 25,26,33,35,39,46,58,62,65,85,93,94,111,118,119,133,134,145,146,155,

%T 161,178,183,202,206,209,214,219,226,235,237,247,249,253,259,265,267,

%U 287,291,295,299,334,335,341,361,362,377,382,386,391,393,395,407,422

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

%C 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 Charles R Greathouse IV, <a href="/A111168/b111168.txt">Table of n, a(n) for n = 1..10000</a>

%F {a(n)} = a(n) is an element of A001358 and 2*a(n)-1 is an element of A001358.

%e n s(n) s*2-1

%e 1 25 = 5^2 49 = 7^2

%e 2 26 = 2 * 13 51 = 3 * 17

%e 3 33 = 3 * 11 65 = 5 * 13

%e 4 35 = 5 * 7 69 = 3 * 23

%e 5 39 = 3 * 13 77 = 7 * 11

%t Select[Range[500],PrimeOmega[#]==2&&PrimeOmega[2#-1]==2&] (* _Harvey P. Dale_, Aug 30 2015 *)

%o (PARI) is(n)=bigomega(n)==2 && bigomega(2*n-1)==2 \\ _Charles R Greathouse IV_, Jan 31 2017

%Y Cf. A001358, A111153, A111170, A111171, A111173, A111176.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Oct 21 2005

%E Extended by _Ray Chandler_, Oct 22 2005