A100045 - OEIS

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A100045

Decimal expansion of 17/24 + log(2).

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

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OFFSET

1,2

COMMENTS

Allouche gives an equality with this constant and an infinite sum involving the sum of the binary digits of numbers. - Charles R Greathouse IV, Sep 08 2012

LINKS

Table of n, a(n) for n=1..102.

Jean-Paul Allouche, Series and infinite products related to binary expansions of integers.

Jean-Paul Allouche and Jeffrey Shallit, Sums of digits and the Hurwitz zeta function, in: K. Nagasaka and E. Fouvry (eds.), Analytic Number Theory, Lecture Notes in Mathematics, Vol. 1434, Springer, Berlin, Heidelberg, 1990, pp. 19-30.

Eric Weisstein's World of Mathematics, Digit Sum.

Index entries for transcendental numbers

FORMULA

Equals Sum_{k>=2} A000120(k)^2 * (8*k^3 + 4*k^2 + k - 1)/(4*k*(k^2-1)*(4*k^2-1)) (Allouche and Shallit, 1990). - Amiram Eldar, Jun 01 2021

EXAMPLE

1.4014805138932786427505654547915099...

MATHEMATICA

RealDigits[17/24+Log[2], 10, 120][[1]] (* Harvey P. Dale, Jan 21 2013 *)

PROG

(PARI) log(2)+17/24 \\ Charles R Greathouse IV, May 15 2019

CROSSREFS

Cf. A000120, A002162.