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 A019774 #91 Mar 01 2025 22:54:41
%S A019774 1,6,4,8,7,2,1,2,7,0,7,0,0,1,2,8,1,4,6,8,4,8,6,5,0,7,8,7,8,1,4,1,6,3,
%T A019774 5,7,1,6,5,3,7,7,6,1,0,0,7,1,0,1,4,8,0,1,1,5,7,5,0,7,9,3,1,1,6,4,0,6,
%U A019774 6,1,0,2,1,1,9,4,2,1,5,6,0,8,6,3,2,7,7,6,5,2,0,0,5,6,3,6,6,6,4
%N A019774 Decimal expansion of sqrt(e).
%C A019774 Also where x^(x^(-2)) is a maximum. - _Robert G. Wilson v_, Oct 22 2014
%C A019774 e^(1/2) maximizes the value of x^(c/(x^2)) for any real positive constant c, and minimizes for it for a negative constant, on the range x > 0. - _A.H.M. Smeets_, Aug 16 2018
%H A019774 Harry J. Smith, <a href="/A019774/b019774.txt">Table of n, a(n) for n = 1..20000</a>
%H A019774 Michael Penn, <a href="https://www.youtube.com/watch?v=FqifDb1_gfc">On means of binomial coefficients.</a>, YouTube video, 2020.
%H A019774 Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007). See p. 522.
%H A019774 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A019774 sqrt(e) = Sum_{n>=0} 1/(2^n*n!) = Sum_{n>=0} 1/(2n)!!. - _Daniel Forgues_, Apr 17 2011
%F A019774 sqrt(e) = 1 + Sum_{n>0} Product_{i=1..n} 1/(2n). - _Ralf Stephan_, Sep 11 2013
%F A019774 Continued fraction representation: sqrt(e) = 1 + 1/(1 + 2/(3 + 4/(5 + ... ))). See A000354 for details. - _Peter Bala_, Jan 30 2015
%F A019774 sqrt(e) = (1/2)*( 1 + (3 + (5 + (7 + ...)/6)/4)/2 ) = 1 + (1 + (1 + (1 + ...)/6)/4)/2. - _Rok Cestnik_, Jan 19 2017
%F A019774 sqrt(e) = 2*Sum_{n >= 0} 1/((1 - 4*n^2)*(2^n)*n!). - _Peter Bala_, Jan 16 2022
%F A019774 sqrt(e) = (16/31)*(1 + Sum_{n>=1} (1/2)^n*((1/2)*n^3 + (1/2)*n + 1)/n!). - _Alexander R. Povolotsky_, Jul 01 2022
%F A019774 sqrt(e) = Sum_{n >= 0} (n + 1/2)/(2^n*n!). - _Peter Bala_, Jun 29 2024
%F A019774 Equals i^(-i/Pi), where i denotes the imaginary unit. - _Stefano Spezia_, Mar 01 2025
%e A019774 1.6487212707001281468486507878141635716537761007101480115750...
%p A019774 evalf(sqrt(exp(1)), 120); # _Muniru A Asiru_, Aug 16 2018
%t A019774 RealDigits[N[Sqrt[E],200]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 21 2011 *)
%o A019774 (PARI) default(realprecision, 20080); x=sqrt(exp(1)); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b019774.txt", n, " ", d)); \\ _Harry J. Smith_, May 01 2009
%Y A019774 Cf. A000354, A001113, A058281 for continued fraction for sqrt(e), A019775.
%K A019774 nonn,cons
%O A019774 1,2
%A A019774 _N. J. A. Sloane_