A078887 - OEIS

%I #13 Nov 12 2020 05:17:20

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

%T 4,8,4,3,2,2,4,3,4,6,8,9,9,3,2,0,3,7,2,9,8,0,7,9,2,3,1,7,4,2,6,7,3,0,

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

%N Decimal expansion of Sum {n>=0} 1/6^(2^n).

%H Aubrey J. Kempner, <a href="https://doi.org/10.1090/S0002-9947-1916-1501054-4">On Transcendental Numbers</a>, Transactions of the American Mathematical Society, volume 17, number 4, October 1916, pages 476-482.

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

%F Equals -Sum_{k>=1} mu(2*k)/(6^k - 1), where mu is the Möbius function (A008683). - _Amiram Eldar_, Jul 12 2020

%e 0.195216644757251284925...

%t RealDigits[ N[ Sum[1/6^(2^n), {n, 0, Infinity}], 110]][[1]]

%o (PARI) suminf(n=0, 1/6^(2^n)) \\ _Michel Marcus_, Nov 11 2020

%Y Cf. A165424.

%Y Similar sums: A007404, A078885, A078585, A078886, A078888, A078889, A078890, A036987.

%K cons,nonn

%O 0,2

%A _Robert G. Wilson v_, Dec 11 2002