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

1,1

Comments

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

Sophie Germain primes are a subsequence, see A005384.

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A068406.

Sequence in context: A032983 A204388 A348255 * A074821 A348511 A338897

Adjacent sequences: A117357 A117358 A117359 * A117361 A117362 A117363

Keyword

nonn

Author

Reinhard Zumkeller, Mar 10 2006

Status

approved