A004676 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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