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A096614 Decimal expansion of Sum_{n>=1} f(2^n)/2^n, where f(n) is the number of even digits in n. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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.

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

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Last modified December 6 14:43 EST 2022. Contains 358644 sequences. (Running on oeis4.)