A004676 Primes written in base 2.

10, 11, 101, 111, 1011, 1101, 10001, 10011, 10111, 11101, 11111, 100101, 101001, 101011, 101111, 110101, 111011, 111101, 1000011, 1000111, 1001001, 1001111, 1010011, 1011001, 1100001, 1100101, 1100111, 1101011, 1101101, 1110001, 1111111, 10000011, 10001001

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base

Comments

The only primes of binary weight 2 are the Fermat primes (only five are known: 11, 101, 10001, 100000001, 10000000000000001); the repunits base 2 are the Mersenne primes. - Daniel Forgues, Nov 07 2011

References

• J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 3.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Chris Caldwell, The prime pages, The first 1000 primes.

Crossrefs

Cf. A019434 Fermat primes (base 10), A000668 Mersenne primes (base 10).

Cf. A174332, A208238, A208241.

Programs

Haskell

a004676 = a007088 . a000040  -- Reinhard Zumkeller, Aug 06 2012

Mathematica

FromDigits /@ IntegerDigits[ Prime[ Range[31]], 2] (* Robert G. Wilson v, Jun 30 2005 *)

PARI

a(n)=subst(Pol(binary(prime(n))), 'x, 10) \\ Charles R Greathouse IV, Mar 20 2013

Formula

a(n) = A007088(A000040(n)). - R. J. Mathar, Jun 03 2011