|
%I #30 Jan 14 2023 13:28:20
%S 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,
%T 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,
%U 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
%N Decimal expansion of Sum_{n>=1} f(2^n)/2^n, where f(n) is the number of even digits in n.
%C 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
%D Jonathan Borwein, David Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, A K Peters, 2004, pp. 14-15.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DigitCount.html">Digit Count</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals -1/9 + Sum_{k>=1} (1 + floor(k * log_10(2)))/2^k. - _Amiram Eldar_, Nov 14 2020
%e 1.03160638...
%t RealDigits[-1/9 + Sum[(1 + Floor[k*Log10[2]])/2^k, {k, 1, 350}], 10,
%t 100][[1]] (* _Amiram Eldar_, Nov 14 2020 *)
%o (PARI) -1/9 + suminf(k=1, (1 + floor(k * log(2)/log(10)))/2^k) \\ _Michel Marcus_, Nov 14 2020
%Y Cf. A055253.
%K nonn,cons,base
%O 1,3
%A _Eric W. Weisstein_, Jun 30 2004
|
