A111176 Sophie Germain 4-almost primes.

40, 220, 580, 712, 808, 812, 904, 940, 1062, 1192, 1444, 1592, 1612, 1690, 1812, 1876, 2002, 2152, 2212, 2236, 2254, 2488, 2502, 2562, 2650, 2662, 2788, 3010, 3052, 3064, 3112, 3162, 3208, 3258, 3272, 3352, 3448, 3550, 3580, 3820, 3832, 3892, 3910, 4012

Offset

1,1

Comments

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.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

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

Example

n p 2*p+1
1 40 = 2^3 * 5 81 = 3^4
2 220 = 2^2 * 5 * 11 441 = 3^2 * 7^2
3 580 = 2^2 * 5 * 29 1161 = 3^3 * 43
4 712 = 2^3 * 89 1425 = 3 * 5^2 * 19
5 808 = 2^3 * 101 1617 = 3 * 7^2 * 11
6 812 = 2^2 * 7 * 29 1625 = 5^3 * 13

Mathematica

Select[Range[5000], PrimeOmega[#]==PrimeOmega[2#+1]==4&] (* Harvey P. Dale, Nov 09 2011 *)

Crossrefs

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

Sequence in context: A247405 A235270 A181637 * A072108 A218404 A235010

Adjacent sequences: A111173 A111174 A111175 * A111177 A111178 A111179

Keyword

easy,nonn

Author

Jonathan Vos Post, Oct 22 2005

Extensions

Extended by Ray Chandler, Oct 22 2005

Status

approved