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

Author

Eric W. Weisstein, Jun 30 2004

Keywords

• nonn
• cons
• base

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

Examples

			1.03160638...
		

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.
• Index entries for transcendental numbers

Crossrefs

Cf. A055253.

Programs

Mathematica

RealDigits[-1/9 + Sum[(1 + Floor[k*Log10[2]])/2^k, {k, 1, 350}], 10,
100][[1]] (* Amiram Eldar, Nov 14 2020 *)

PARI

-1/9 + suminf(k=1, (1 + floor(k * log(2)/log(10)))/2^k) \\ Michel Marcus, Nov 14 2020

Formula

Equals -1/9 + Sum_{k>=1} (1 + floor(k * log_10(2)))/2^k. - Amiram Eldar, Nov 14 2020