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A048649 Decimal expansion of Sum_{m>=0} 1/(2^2^m - 1).

%I A048649 #20 Nov 26 2024 17:13:58
%S A048649 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 A048649 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 A048649 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 A048649 Decimal expansion of Sum_{m>=0} 1/(2^2^m - 1).
%H A048649 Harry J. Smith, <a href="/A048649/b048649.txt">Table of n, a(n) for n = 1..20000</a>
%H A048649 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A048649 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 A048649 1.40393682788217832057620607413720935453...
%t A048649 NSum[1/(2^2^m - 1), {m, 0, Infinity}, WorkingPrecision -> 99] // RealDigits // First (* _Jean-François Alcover_, Feb 12 2013 *)
%o A048649 (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 A048649 + A051158 = 2.
%Y A048649 Cf. A007814, A048164, A048650.
%K A048649 nonn,cons
%O A048649 1,2
%A A048649 _N. J. A. Sloane_
%E A048649 Deleted old PARI program. - _Harry J. Smith_, May 20 2009