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 A007493 M0036 #43 Feb 16 2025 08:32:31
%S A007493 2,0,9,4,5,5,1,4,8,1,5,4,2,3,2,6,5,9,1,4,8,2,3,8,6,5,4,0,5,7,9,3,0,2,
%T A007493 9,6,3,8,5,7,3,0,6,1,0,5,6,2,8,2,3,9,1,8,0,3,0,4,1,2,8,5,2,9,0,4,5,3,
%U A007493 1,2,1,8,9,9,8,3,4,8,3,6,6,7,1,4,6,2,6,7,2,8,1,7,7,7,1,5,7,7,5,7,8,6,0,8,3
%N A007493 Decimal expansion of Wallis's number, the real root of x^3 - 2*x - 5.
%C A007493 "The real solution to the equation x^3 - 2x - 5 = 0. This equation was solved by [the English mathematician John] Wallis [1616-1703] to illustrate Newton's method for the numerical solution of equations.
%C A007493 "It has since served as a test for many subsequent methods of approximation and its real root is now known to 4000 digits." [Gruenberger]
%D A007493 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A007493 D. E. Smith, A Source Book in Mathematics, McGraw-Hill, 1929, pp. 247-248.
%D A007493 David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 27.
%H A007493 Harry J. Smith, <a href="/A007493/b007493.txt">Table of n, a(n) for n = 1..20000</a>
%H A007493 Fred Gruenberger, <a href="https://www.jstor.org/stable/24969338">How to handle numbers with thousands of digits, and why one might want to</a>, Computer Recreations, Scientific American, 250 (No. 4, 1984), 19-26.
%H A007493 W. G. Horner, <a href="http://www.jstor.org/stable/107508">A new method of solving numerical equations of all orders, by continuous approximation</a>, Phil. Trans. Royal Soc., 1819, pp. 308-335.
%H A007493 D. Olivastro, <a href="/A007493/a007493.pdf">Ancient Puzzles</a>, Bantam Books, NY (1993), cover page and pp. 58-59. (Annotated scanned copy)
%H A007493 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WallissConstant.html">Wallis's Constant</a>
%H A007493 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>
%F A007493 Equals (5/2 - sqrt(643/108))^(1/3) + (5/2 + sqrt(643/108))^(1/3). - _Michal Paulovic_, Mar 19 2023
%e A007493 2.094551481542326591482386540579302963857306105628239180304128529...
%t A007493 RealDigits[ N[ 1/3* (135/2 - (3*Sqrt[1929])/2)^(1/3) + (1/2*(45 + Sqrt[1929]) )^(1/3) / 3^(2/3), 100]][[1]]
%o A007493 (PARI) default(realprecision, 20080); x=NULL; p=x^3 - 2*x - 5; rs=polroots(p); r=real(rs[1]); for (n=1, 20000, d=floor(r); r=(r-d)*10; write("b007493.txt", n, " ", d)); \\ _Harry J. Smith_, May 03 2009
%o A007493 (PARI) polrootsreal(x^3-2*x-5)[1] \\ _Charles R Greathouse IV_, Apr 14 2014
%Y A007493 Cf. A058297 (continued fraction).
%K A007493 cons,nonn
%O A007493 1,1
%A A007493 _N. J. A. Sloane_, _Robert G. Wilson v_
%E A007493 Final digits of sequence corrected using the b-file. - _N. J. A. Sloane_, Aug 30 2009