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Decimal expansion of lim_{n->infinity} (1 - 1/2)^((1/2 - 1/3)^(...^(1/(2n-1) - 1/(2n)))).
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%I #35 Nov 20 2019 06:15:06

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

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

%U 8,4,4,7,9,8,0,2,7,1,4,8,2,8,7,9,0,8,8

%N Decimal expansion of lim_{n->infinity} (1 - 1/2)^((1/2 - 1/3)^(...^(1/(2n-1) - 1/(2n)))).

%C The sequence of real values x(n) = (1 - 1/2)^((1/2 - 1/3)^(...^(1/n - 1/(n+1)))) converges to two different limits depending on whether n is even or odd. This integer sequence gives the decimal expansion of the lower limit, to which the odd-indexed terms of {x(n)} converge.

%H Zeraoulia Rafik, <a href="https://math.stackexchange.com/q/2822112/156150">Question on Math Stackexchange</a>

%e 0.56778606544394002098000796382530333102219963214865...

%o (PARI) my(N=99,y=(1/(N*(N+1)))); forstep(n=N-1,1,-1,y=1/(n*(n+1))^y); y \\ _Michel Marcus_, Nov 08 2019

%Y Cf. A328942.

%K nonn,cons

%O 0,1

%A _R Zeraoulia_, Oct 31 2019

%E More terms from _Jon E. Schoenfield_, Nov 02 2019