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

Author

Jonathan Vos Post, Mar 24 2009

Keywords

• nonn
• base
• more

Comments

From Table 1, p. 2, of Kak.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000040, A004676, A036378.

Programs

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

Extensions

a(28) from Washington Bomfim, Jan 19 2011