A117293 Mersenne primes written in binary.

11, 111, 11111, 1111111, 1111111111111, 11111111111111111, 1111111111111111111, 1111111111111111111111111111111, 1111111111111111111111111111111111111111111111111111111111111

Offset: 1

Author

Jacob Vecht, Apr 23 2006

Keywords

• base
• nonn

Comments

The number of bits in a(n) is equal to A000043(n). - Omar E. Pol, Feb 22 2008

Examples

			The third Mersenne prime is 31, i.e., 11111 in binary.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..14
• Wikipedia, Mersenne prime.

Crossrefs

Cf. A000043, A000668, A007088.

Programs

Mathematica

Map[(10^# - 1)/9 &, MersennePrimeExponent[Range[9]]] (* Amiram Eldar, Oct 22 2024 *)

PARI

apply(p->fromdigits(binary(p)), select(isprime, vector(20,n,2^prime(n)-1))) \\ Charles R Greathouse IV, Sep 14 2016

Formula

a(n) = A007088(A000668(n)). - Amiram Eldar, Oct 22 2024