A096614 Decimal expansion of Sum_{n>=1} f(2^n)/2^n, where f(n) is the number of even digits in n.

1, 0, 3, 1, 6, 0, 6, 3, 8, 6, 4, 4, 5, 0, 9, 6, 1, 2, 2, 5, 1, 5, 4, 7, 7, 3, 5, 4, 1, 8, 7, 1, 3, 0, 3, 1, 0, 3, 9, 0, 2, 2, 6, 4, 1, 5, 2, 9, 2, 6, 9, 4, 0, 7, 0, 9, 5, 7, 6, 7, 3, 2, 4, 1, 2, 1, 1, 1, 0, 7, 2, 8, 3, 9, 2, 1, 4, 0, 7, 8, 9, 1, 6, 0, 5, 5, 6, 1, 7, 2, 3, 7, 5, 1, 1, 2, 0, 6, 8, 2, 4, 0, 0, 2, 5, 5

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

Table of n, a(n) for n=1..106.

Eric Weisstein's World of Mathematics, Digit Count.

Index entries for transcendental numbers

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

Cf. A055253.

Sequence in context: A298330 A210621 A226771 * A011002 A298241 A113817

Adjacent sequences: A096611 A096612 A096613 * A096615 A096616 A096617

Keyword

nonn,cons,base

Author

Eric W. Weisstein, Jun 30 2004

Status

approved