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A062542 Decimal expansion of the continued fraction constant (base 10). 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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 (ln 2) (ln 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 * A109693 A188858 A199610

Adjacent sequences:  A062539 A062540 A062541 * A062543 A062544 A062545

KEYWORD

cons,easy,nonn

AUTHOR

Jason Earls (zevi_35711(AT)yahoo.com), Jun 25 2001

STATUS

approved

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Last modified October 1 00:26 EDT 2014. Contains 247498 sequences.