A100045 - OEIS

%I #23 Nov 18 2023 06:28:23

%S 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,

%T 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,

%U 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

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

%C 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

%H Jean-Paul Allouche, <a href="http://algo.inria.fr/seminars/sem92-93/allouche.pdf">Series and infinite products related to binary expansions of integers</a>.

%H Jean-Paul Allouche and Jeffrey Shallit, <a href="https://doi.org/10.1007/BFb0097122">Sums of digits and the Hurwitz zeta function</a>, in: K. Nagasaka and E. Fouvry (eds.), Analytic Number Theory, Lecture Notes in Mathematics, Vol. 1434, Springer, Berlin, Heidelberg, 1990, pp. 19-30.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DigitSum.html">Digit Sum</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F 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

%e 1.4014805138932786427505654547915099...

%t RealDigits[17/24+Log[2],10,120][[1]] (* _Harvey P. Dale_, Jan 21 2013 *)

%o (PARI) log(2)+17/24 \\ _Charles R Greathouse IV_, May 15 2019

%Y Cf. A000120, A002162.

%K nonn,cons,easy

%O 1,2

%A _Eric W. Weisstein_, Oct 31 2004