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).

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.

Links

Table of n, a(n) for n=0..86.

Example

-0.27685762486257653893643725082357339631797973752751373915977316435485014180...

Crossrefs

Cf. A073833, A232975.

Sequence in context: A189959 A158241 A156591 * A138283 A308682 A117968

Adjacent sequences: A233767 A233768 A233769 * A233771 A233772 A233773

Keyword

nonn,cons

Author

Jon E. Schoenfield and N. J. A. Sloane, Dec 15 2013

Status

approved