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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).
3
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, 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, 0, 1, 4, 1, 8, 0, 8, 2, 9, 7, 1, 2, 4, 3, 1, 1, 8, 9, 8
OFFSET
0,1
COMMENTS
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 = (log c1)/2 where c1 is a constant described in the comments in A073833; its digits are in A232975.
EXAMPLE
-0.27685762486257653893643725082357339631797973752751373915977316435485014180...
CROSSREFS
Sequence in context: A189959 A158241 A156591 * A138283 A308682 A117968
KEYWORD
nonn,cons
AUTHOR
STATUS
approved