A062542 Decimal expansion of the continued fraction constant (base 10).

1, 0, 3, 0, 6, 4, 0, 8, 3, 4, 1, 0, 0, 7, 1, 2, 9, 3, 5, 8, 8, 1, 7, 7, 6, 0, 9, 4, 1, 1, 6, 9, 3, 6, 8, 4, 0, 9, 2, 5, 9, 2, 0, 3, 1, 1, 1, 2, 0, 7, 2, 6, 2, 8, 1, 7, 7, 0, 0, 6, 0, 9, 5, 2, 2, 3, 4, 9, 5, 4, 4, 2, 8, 0, 0, 4, 7, 9, 9, 7, 6, 7, 5, 1, 8, 3, 6, 0, 8, 0, 8, 3, 9, 5, 6, 5, 8, 6, 5, 4, 7, 6, 2, 6, 3

Offset

1,3

Comments

"(By strange coincidence, the information in a typical continued fraction term is very nearly one decimal digit - actually pi^2/(6 (ln 2) (ln 10)) = 1.0306.) R. W. Gosper. Math-Fun list, April 9, 1998. This constant is the average number of decimal digits necessary to have the equivalent continued fraction representations of a number in base 10. In other words if you have N decimal digits it will give you N/C = N/1.0306 valid partial quotients in average." - Simon Plouffe

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.8 Khintchine-Lévy constants, p. 60.

Links

Table of n, a(n) for n=1..105.

Simon Plouffe, Plouffe's Inverter

Eric Weisstein's World of Mathematics, Lochs' Theorem

Formula

Pi^2/(6 (log 2) (log 10)).

Example

1.03064083410071293588177609411693684092592031112072628177006095223495442800479...

Mathematica

RealDigits[Pi^2/(6Log[2]Log[10]), 10, 120][[1]] (* Harvey P. Dale, Apr 11 2012 *)

Crossrefs

Cf. A062543.

Sequence in context: A215664 A088162 A133170 * A360173 A109693 A188858

Adjacent sequences: A062539 A062540 A062541 * A062543 A062544 A062545

Keyword

cons,easy,nonn

Author

Jason Earls, Jun 25 2001

Status

approved