A033260 Continued fraction for Laplace's limit constant.

0, 1, 1, 1, 27, 1, 1, 1, 8, 2, 154, 2, 4, 1, 5, 1, 1, 2, 1601, 2, 63, 1, 2, 12, 17, 9, 2, 1, 1, 57, 1, 6, 2, 4, 3, 10, 1, 6, 2, 1, 3, 4, 2, 1, 31, 3, 6, 1, 1, 4, 2, 1, 1, 1, 1, 1, 1, 14, 1, 4, 1, 2, 2, 1, 97, 1, 52, 2, 4, 1, 1, 5, 13, 1, 1, 3, 6, 2, 3, 3, 2, 2, 1, 1, 2, 28, 2, 3, 1, 4, 2, 1, 4

Offset: 0

Author

Eric W. Weisstein

Keywords

• nonn
• cofr

References

• S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 266-268.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..20000
• S. R. Finch, Laplace Limit Constant
• Eric Weisstein's World of Mathematics, Laplace Limit

Crossrefs

Cf. A033259 (decimal expansion), A033261, A033262, A033263.

Programs

Mathematica

ContinuedFraction[Sqrt[x^2-1]/.FindRoot[x==Coth[x], {x,1}, WorkingPrecision -> 250], 121] (* G. C. Greubel, Dec 13 2024 *)

Extensions

Offset changed by Andrew Howroyd, Jul 04 2024