OFFSET
1,3
COMMENTS
This constant is transcendental. If the number of even digits is replaced with the number of odd digits, then the sum will be 1/9. (Borwein et al. 2004). - Amiram Eldar, Nov 14 2020
REFERENCES
Jonathan Borwein, David Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, A K Peters, 2004, pp. 14-15.
LINKS
Eric Weisstein's World of Mathematics, Digit Count.
FORMULA
Equals -1/9 + Sum_{k>=1} (1 + floor(k * log_10(2)))/2^k. - Amiram Eldar, Nov 14 2020
EXAMPLE
1.03160638...
MATHEMATICA
RealDigits[-1/9 + Sum[(1 + Floor[k*Log10[2]])/2^k, {k, 1, 350}], 10,
100][[1]] (* Amiram Eldar, Nov 14 2020 *)
PROG
(PARI) -1/9 + suminf(k=1, (1 + floor(k * log(2)/log(10)))/2^k) \\ Michel Marcus, Nov 14 2020
CROSSREFS
KEYWORD
AUTHOR
Eric W. Weisstein, Jun 30 2004
STATUS
approved