cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A062542 #26 Jul 04 2025 18:35:49
%S A062542 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,
%T A062542 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,
%U A062542 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
%N A062542 Decimal expansion of the continued fraction constant (base 10).
%C A062542 "(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_
%D A062542 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.8 Khintchine-Lévy constants, p. 60.
%H A062542 Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/continuedfr.txt">Plouffe's Inverter</a>.
%H A062542 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LochsTheorem.html">Lochs' Theorem</a>.
%F A062542 Equals Pi^2/(6 (log 2) (log 10)).
%F A062542 Equals A013661/(A002162*A002392). - _Stefano Spezia_, Nov 16 2024
%e A062542 1.03064083410071293588177609411693684092592031112...
%t A062542 RealDigits[Pi^2/(6Log[2]Log[10]),10,120][[1]] (* _Harvey P. Dale_, Apr 11 2012 *)
%o A062542 (PARI) Pi^2/(6*log(2)*log(10)) \\ _Stefano Spezia_, Nov 16 2024
%Y A062542 Cf. A062543.
%Y A062542 Cf. A002162, A002392, A013661.
%K A062542 cons,easy,nonn
%O A062542 1,3
%A A062542 _Jason Earls_, Jun 25 2001