A158671 Frequency of 0's in a constant bit representation of primes.

1, 4, 10, 23, 47, 100, 202, 403, 798, 1592, 3171, 6293, 12578, 24987, 49796, 99190, 197699, 394227, 785804, 1567419, 3127966, 6242519, 12464093, 24887586, 49698098, 99261034, 198285886

Offset

2,2

Comments

From Table 1, p. 2, of Kak.

Links

Table of n, a(n) for n=2..28.

Subhash Kak, Prime Reciprocal Digit Frequencies and the Euler Zeta Function, arXiv:0903.3904 [math.GM], 2009.

Example

The number of 0's and 1's for all primes with respect to different binary lengths from 2 to 27 is given in Table 1. Thus for all primes of binary length 3, we have the primes 2, 3, 5, and 7 which in the binary form are 010, 011, 101, and 111, with four 0's and 8 1's, so a(2) = 4. Likewise, for all primes of bit length 4, we count the primes 2, 3, 5, 7, 11, and 13 corresponding to the sequences 0010, 0011, 0101, 0111, 1011, 1101, which gives us ten 0's and 14 1's, so a(3) = 10.

Prog

(PARI) an=0; c=0;
f(n)={i=2^(n-1); j=2^n - 1; z=0; for(k=i, j, if(isprime(k), c++; v=binary(k); L=#v; for(m=1, L, if(v[m]==0, z++)))); return(z)};
an=f(2); print1(an, ", "); for(n=3, 28, an=an+c+f(n); print1(an, ", ")) \\ Washington Bomfim, Jan 19 2011

Crossrefs

Cf. A000040, A004676, A036378.

Sequence in context: A008268 A084446 A209815 * A001980 A266376 A057750

Adjacent sequences: A158668 A158669 A158670 * A158672 A158673 A158674

Keyword

nonn,base,more

Author

Jonathan Vos Post, Mar 24 2009

Extensions

a(28) from Washington Bomfim, Jan 19 2011

Status

approved