A062542 -id:A062542 - cp's OEIS frontend

A062543 Continued fraction expansion of continued fractions constant (base 10).

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

Offset: 0

Jason Earls, Jun 25 2001

a(n) = A086820(n+1) since Lochs constant = 1/continued fractions constant. - Gerald McGarvey, Aug 02 2004

Simon Plouffe, 5000 digits of 1.03064...

Cf. A062542.

PARI
```
contfrac(Pi^2/(6*(log(2))*(log(10)))).
```

A086819 Decimal expansion of Lochs's constant.

Original entry on oeis.org

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

Offset: 0

Benoit Cloitre, Aug 06 2003

Named after the Austrian mathematician Gustav Emil Maria Johannes Lochs (1907-1988). - Amiram Eldar, Feb 05 2022

			0.97027011439203392574025601921001083378128470478516...

Dan Lascu and Gabriela Ileana Sebe, Comparison of various continued fraction expansions: a Lochs-type approach, arXiv:2005.00380 [math.NT], 2020.
Gustav Lochs, Vergleich der Genauigkeit von Dezimalbruch und Kettenbruch, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Volume 27, Issue 1-2 (April 1964), pp. 142-144.
Eric Weisstein's World of Mathematics, Lochs' Constant.
Eric Weisstein's World of Mathematics, Lochs' Theorem.

Cf. A062542, A240995.

RealDigits[(6*Log[2]Log[10])/Pi^2,10,120][[1]] (* Harvey P. Dale, Jul 13 2019 *)

6*log(2)*log(10)/Pi^2 \\ Michel Marcus, Oct 17 2014

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

Equals 1/A062542 = 1/(2*A240995). - Amiram Eldar, Feb 05 2022

cp's OEIS Frontend

A062543 Continued fraction expansion of continued fractions constant (base 10).

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