A117360 Numbers m such that m and 2*m+1 have the same number of prime factors.

2, 3, 4, 5, 10, 11, 23, 25, 29, 34, 38, 40, 41, 46, 52, 53, 55, 57, 76, 77, 83, 89, 91, 93, 106, 113, 118, 123, 129, 130, 131, 133, 143, 145, 159, 161, 169, 171, 172, 173, 177, 179, 185, 191, 201, 203, 205, 206, 212, 213, 218, 220, 226, 233, 235, 238, 239, 251

Offset: 1

Author

Reinhard Zumkeller, Mar 10 2006

Keywords

• nonn

Comments

A001222(a(n)) = A001222(2*a(n)+1);

Sophie Germain primes are a subsequence, see A005384.

Examples

			m=52=2*2*13, 2*52+1=105=3*5*7, therefore 52 is a term.
		

Links

• R. Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A068406.

Programs

Mathematica

Select[Range[255], PrimeOmega[#] == PrimeOmega[2 # + 1] &] (* Ivan Neretin, Apr 30 2016 *)

PARI

is(n)=bigomega(n)==bigomega(2*n+1) \\ Charles R Greathouse IV, Apr 30 2016