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Decimal expansion of lim_{n -> infinity} b(n)^2 - 2n - (log n)/2 where b(i) = b(i-1) + 1/b(i-1) for i >= 2, b(1) = 1 (see A073833).
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%I #18 Feb 10 2020 02:16:55

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

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

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

%N Decimal expansion of lim_{n -> infinity} b(n)^2 - 2n - (log n)/2 where b(i) = b(i-1) + 1/b(i-1) for i >= 2, b(1) = 1 (see A073833).

%C b(n)^2 = t/2 + u + (u - 1/2)/t + (-u^2 + 2*u - 11/12)/t^2 + (4*u^3/3 - 5*u^2 + 17*u/3 - 65/36)/t^3 + ... where t=4*n, u=(log n)/2+c, and c=-0.27685762486257653893643725082....

%C c = (log c1)/2 where c1 is a constant described in the comments in A073833; its digits are in A232975.

%e -0.27685762486257653893643725082357339631797973752751373915977316435485014180...

%Y Cf. A073833, A232975.

%K nonn,cons

%O 0,1

%A _Jon E. Schoenfield_ and _N. J. A. Sloane_, Dec 15 2013