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.
%I A094641 #20 May 27 2025 12:26:54 %S A094641 0,4,7,6,3,1,1,9,1,1,4,26,1,2,4,1,9,1,20,3,1,12,1,2,7,1,5,2,1,5,3,1,1, %T A094641 1,4,1,1,57,1,2,1,8,8,1,1,1,1,1,22,1,1,6,1,6,6,1,3,1,4,2,2,2,4,1,1,2, %U A094641 1,19,17,348,1,1,5,16,2,2,5,1,5,2,4,2,5,1,11,1,1,11,13,2,1,1,5,2,1,2,10,1,2 %N A094641 Continued fraction for the "alternating Euler constant" log(4/Pi). %C A094641 See the Comments in A094640 for why log(4/Pi) is an "alternating Euler constant." %D A094641 G. Boros and V. Moll, Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge University Press, Cambridge, 2004, Chap. 7. %D A094641 J. Borwein and P. Borwein, Pi and the AGM, John Wiley & Sons, New York, 1987, Chap. 11. %H A094641 D. Huylebrouck, <a href="https://web.archive.org/web/20240530051920/https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Huylebrouck222-231.pdf">Similarities in irrationality proofs for Pi, ln2, zeta(2) and zeta(3)</a>, Amer. Math. Monthly 108 (2001) 222-231. %H A094641 Jonathan Sondow, <a href="https://arxiv.org/abs/math/0211148">Double Integrals for Euler's Constant and ln(4/Pi) and an Analog of Hadjicostas's Formula</a>, arXiv:math/0211148 [math.CA], 2002-2004; Amer. Math. Monthly 112 (2005) 61-65. %H A094641 Jonathan Sondow, <a href="https://arxiv.org/abs/math/0508042">New Vacca-Type Rational Series for Euler's Constant and Its "Alternating" Analog ln(4/Pi)</a>, arXiv:math/0508042 [math.NT], 2005; Additive Number Theory, Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson (D. Chudnovsky and G. Chudnovsky, eds.), Springer, 2010, pp. 331-340. %H A094641 Jonathan Sondow and Petros Hadjicostas, <a href="http://arXiv.org/abs/math/0610499">The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant</a>, arXiv:math/0610499 [math.CA], 2006; J. Math. Anal. Appl. 332 (1) (2007), 292-314. %e A094641 log(4/Pi) = 0 + 1/(4 + 1/(7 + 1/(6 + 1/(3 + 1/(1 + ...))))) %t A094641 ContinuedFraction[ Log[4/Pi], 100] %Y A094641 Cf. A094640 (decimal expansion of log(4/Pi)). %K A094641 cofr,easy,nonn %O A094641 0,2 %A A094641 _Jonathan Sondow_ and _Robert G. Wilson v_, May 18 2004 %E A094641 Offset changed by _Andrew Howroyd_, Aug 07 2024