A111176 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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