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

1,1

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.

Formula

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

Mathematica

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

Prog

(Haskell)
a004676 = a007088 . a000040  -- Reinhard Zumkeller, Aug 06 2012
(PARI) a(n)=subst(Pol(binary(prime(n))), 'x, 10) \\ Charles R Greathouse IV, Mar 20 2013

Crossrefs

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

Cf. A174332, A208238, A208241.

Sequence in context: A230297 A086084 A206073 * A303593 A124387 A171796

Adjacent sequences: A004673 A004674 A004675 * A004677 A004678 A004679

Keyword

nonn,easy,base

Author

N. J. A. Sloane

Status

approved