cp's OEIS Frontend

A233770 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).

%I A233770 #18 Feb 10 2020 02:16:55
%S A233770 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 A233770 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 A233770 0,1,4,1,8,0,8,2,9,7,1,2,4,3,1,1,8,9,8
%N A233770 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 A233770 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 A233770 c = (log c1)/2 where c1 is a constant described in the comments in A073833; its digits are in A232975.
%e A233770 -0.27685762486257653893643725082357339631797973752751373915977316435485014180...
%Y A233770 Cf. A073833, A232975.
%K A233770 nonn,cons
%O A233770 0,1
%A A233770 _Jon E. Schoenfield_ and _N. J. A. Sloane_, Dec 15 2013