

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
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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. 1415.


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



