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

25, 26, 33, 35, 39, 46, 58, 62, 65, 85, 93, 94, 111, 118, 119, 133, 134, 145, 146, 155, 161, 178, 183, 202, 206, 209, 214, 219, 226, 235, 237, 247, 249, 253, 259, 265, 267, 287, 291, 295, 299, 334, 335, 341, 361, 362, 377, 382, 386, 391, 393, 395, 407, 422

Offset: 1

Author

Jonathan Vos Post, Oct 21 2005

Keywords

• easy
• nonn

Comments

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.

Examples

			n s(n) s*2-1
1 25 = 5^2 49 = 7^2
2 26 = 2 * 13 51 = 3 * 17
3 33 = 3 * 11 65 = 5 * 13
4 35 = 5 * 7 69 = 3 * 23
5 39 = 3 * 13 77 = 7 * 11
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

Select[Range[500],PrimeOmega[#]==PrimeOmega[2#-1]==2&]  (* Harvey P. Dale, Jul 23 2025 *)

PARI

is(n)=bigomega(n)==2 && bigomega(2*n-1)==2 \\ Charles R Greathouse IV, Jan 31 2017

Formula

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

Extensions

Extended by Ray Chandler, Oct 22 2005