%I #17 Nov 06 2020 08:36:24

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

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

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

%N Decimal expansion of Sum_{m>=0} 1/(2^2^m - 1).

%H Harry J. Smith, <a href="/A048649/b048649.txt">Table of n, a(n) for n = 1..20000</a>

%F Equals 1 + Sum_{n>=1} A007814(n)/2^n = 4/3 + Sum_{n>=1} A007814(n)/4^n = 7/5 + Sum_{n>=1} A007814(n)/16^n. - _Amiram Eldar_, Nov 06 2020

%e 1.40393682788217832057620607413720935453...

%t NSum[1/(2^2^m - 1), {m, 0, Infinity}, WorkingPrecision -> 99] // RealDigits // First (* _Jean-François Alcover_, Feb 12 2013 *)

%o (PARI) { default(realprecision, 20080); x=suminf(m=0, 1/(2^2^m - 1)); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b048649.txt", n, " ", d)); } \\ _Harry J. Smith_, May 07 2009

%Y A048649 + A051158 = 2.

%Y Cf. A007814, A048164, A048650.

%K nonn,cons

%O 1,2

%A _N. J. A. Sloane_

%E Deleted old PARI program. - _Harry J. Smith_, May 20 2009