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

Offset: 1

Author

Eric W. Weisstein, Oct 31 2004

Keywords

• nonn
• cons
• easy

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

Examples

			1.4014805138932786427505654547915099...
		

Links

• 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

Crossrefs

Cf. A000120, A002162.

Programs

Mathematica

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

PARI

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

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