

A158671


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


1



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



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, Mar 23, 2009.


EXAMPLE

The number of 0's and 1's for all primes of 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^(n1); 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.
Sequence in context: A008268 A084446 A209815 * A001980 A266376 A057750
Adjacent sequences: A158668 A158669 A158670 * A158672 A158673 A158674


KEYWORD

base,easy,nonn


AUTHOR

Jonathan Vos Post, Mar 24 2009


EXTENSIONS

a(28) from Washington Bomfim


STATUS

approved



