A117293 - OEIS

%I #18 Oct 22 2024 05:43:18

%S 11,111,11111,1111111,1111111111111,11111111111111111,

%T 1111111111111111111,1111111111111111111111111111111,

%U 1111111111111111111111111111111111111111111111111111111111111

%N Mersenne primes written in binary.

%C The number of bits in a(n) is equal to A000043(n). - _Omar E. Pol_, Feb 22 2008

%H Amiram Eldar, <a href="/A117293/b117293.txt">Table of n, a(n) for n = 1..14</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Mersenne_prime">Mersenne prime</a>.

%F a(n) = A007088(A000668(n)). - _Amiram Eldar_, Oct 22 2024

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

%t Map[(10^# - 1)/9 &, MersennePrimeExponent[Range[9]]] (* _Amiram Eldar_, Oct 22 2024 *)

%o (PARI) apply(p->fromdigits(binary(p)), select(isprime, vector(20,n,2^prime(n)-1))) \\ _Charles R Greathouse IV_, Sep 14 2016

%Y Cf. A000043, A000668, A007088.

%K base,nonn

%O 1,1

%A _Jacob Vecht_, Apr 23 2006