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

Author

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

Keywords

• nonn
• cons

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.

Examples

			-0.27685762486257653893643725082357339631797973752751373915977316435485014180...
		

Crossrefs

Cf. A073833, A232975.