%I #8 Nov 21 2013 12:48:44

%S 40,220,580,712,808,812,904,940,1062,1192,1444,1592,1612,1690,1812,

%T 1876,2002,2152,2212,2236,2254,2488,2502,2562,2650,2662,2788,3010,

%U 3052,3064,3112,3162,3208,3258,3272,3352,3448,3550,3580,3820,3832,3892,3910,4012

%N Sophie Germain 4-almost primes.

%C 4-almost primes P such that 2*P + 1 are also 4-almost primes. There should also be 4-almost prime chains of length k analogous to Cunningham chains of the first kind and Tomaszewski chains of the first kind. A 4-almost prime chain of length k is a sequence of 4-almost primes a(1) < a(2) < ... < a(k) such that a(i+1) = 2*a(i) + 1 for i = 1, ..., k-1. There are no such chains beginning with integers under 1200.

%H Harvey P. Dale, <a href="/A111176/b111176.txt">Table of n, a(n) for n = 1..1000</a>

%F {a(n)} = a(n) is an element of A014613 and 2*a(n)+1 is an element of A014613.

%e n p 2*p+1

%e 1 40 = 2^3 * 5 81 = 3^4

%e 2 220 = 2^2 * 5 * 11 441 = 3^2 * 7^2

%e 3 580 = 2^2 * 5 * 29 1161 = 3^3 * 43

%e 4 712 = 2^3 * 89 1425 = 3 * 5^2 * 19

%e 5 808 = 2^3 * 101 1617 = 3 * 7^2 * 11

%e 6 812 = 2^2 * 7 * 29 1625 = 5^3 * 13

%t Select[Range[5000],PrimeOmega[#]==PrimeOmega[2#+1]==4&] (* _Harvey P. Dale_, Nov 09 2011 *)

%Y Cf. A005384, A014613, A111153, A111168, A111170, A111171, A111173.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Oct 22 2005

%E Extended by _Ray Chandler_, Oct 22 2005