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 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 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^(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. 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

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)