A086819 Decimal expansion of Lochs's constant.

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

0,1

Comments

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

Links

Table of n, a(n) for n=0..103.

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.

Formula

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

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

Example

0.97027011439203392574025601921001083378128470478516...

Mathematica

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

Prog

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

Crossrefs

Cf. A062542, A240995.

Sequence in context: A185364 A085678 A256687 * A019885 A199078 A194098

Adjacent sequences: A086816 A086817 A086818 * A086820 A086821 A086822

Keyword

cons,nonn

Author

Benoit Cloitre, Aug 06 2003

Status

approved