A248853 - OEIS

%I #14 Jan 17 2020 16:19:34

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

%T 4,4,5,5,7,8,2,0,4,0,3,1,4,8,7,5,2,5,0,9,2,5,2,1,4,7,5,2,0,7,7,4,0,1,

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

%N Decimal expansion of a second variant of the Komornik-Loreti constant.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.8 Prouhet-Thue-Morse Constant, p. 438.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 56.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Komornik-LoretiConstant.html">Komornik-Loreti Constant</a>

%F The number 'q' is the unique positive solution of Sum_{n >= 1} (1-t(n))*q^-n = 1, where t(n) = A010060(n).

%e 2.910016055655574691986036509619791445578204031487525...

%t RealDigits[ q /. FindRoot[ Sum[(1 + Mod[DigitCount[n, 2, 1], 2])/q^n, {n, 1, 2000}] == 1, {q, 3}, WorkingPrecision -> 120], 10, 100] // First

%Y Cf. A010060, A055060, A248852.

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, Mar 03 2015