A062543 -id:A062543 - cp's OEIS frontend

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

Jason Earls, Jun 25 2001

"(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, Apr 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

			1.03064083410071293588177609411693684092592031112...

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

Simon Plouffe, Plouffe's Inverter.
Eric Weisstein's World of Mathematics, Lochs' Theorem.

Cf. A062543.

Cf. A002162, A002392, A013661.

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

Pi^2/(6*log(2)*log(10)) \\ Stefano Spezia, Nov 16 2024

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

Equals A013661/(A002162*A002392). - Stefano Spezia, Nov 16 2024

A086820 Continued fraction expansion of Lochs constant.

Original entry on oeis.org

0, 1, 32, 1, 1, 1, 2, 1, 46, 7, 2, 7, 10, 8, 1, 71, 1, 37, 1, 1, 23, 5, 1, 1, 5, 11, 1, 5, 3, 1, 1, 2, 115, 1, 21, 3, 3, 1, 4, 39, 1, 2, 3, 26, 1, 4, 1, 1, 1, 1, 7, 1, 49, 1, 2, 1, 6, 1, 5, 40, 1, 1, 1, 7, 6, 2, 15, 6, 20, 7, 3, 6, 2, 2, 2, 2, 1, 3, 1, 3, 1, 1, 1, 1, 1, 4, 159, 1, 1, 35, 2, 1, 2, 2, 1, 1, 1

Offset: 0

Benoit Cloitre, Aug 06 2003

a(n+1) = A062543(n) since Lochs constant = 1/continued fractions constant. - Gerald McGarvey, Aug 02 2004

Eric Weisstein's World of Mathematics, Lochs theorem.

ContinuedFraction[(6 Log[2]Log[10])/Pi^2,100] (* Harvey P. Dale, Jul 19 2013 *)

Lochs constant = 6*log(2)*log(10)/Pi^2 = 0.9702701143920339257...

cp's OEIS Frontend

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

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