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 A092605 #37 Apr 22 2025 12:21:01
%S A092605 6,0,6,5,3,0,6,5,9,7,1,2,6,3,3,4,2,3,6,0,3,7,9,9,5,3,4,9,9,1,1,8,0,4,
%T A092605 5,3,4,4,1,9,1,8,1,3,5,4,8,7,1,8,6,9,5,5,6,8,2,8,9,2,1,5,8,7,3,5,0,5,
%U A092605 6,5,1,9,4,1,3,7,4,8,4,2,3,9,9,8,6,4,7,6,1,1,5,0,7,9,8,9,4,5,6,0,2,6,4,2,3
%N A092605 Decimal expansion of e^(-1/2) or 1/sqrt(e).
%C A092605 For x = e^(-1/2), the largest prime factor of a random integer n is equally likely to be above or below n^x. - _Charles R Greathouse IV_, May 25 2009
%C A092605 Siegel's conjecture: this constant gives the density of regular primes among all the primes (see Ribenboim and Siegel). - _Stefano Spezia_, Apr 22 2025
%D A092605 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 225.
%D A092605 C. L. Siegel, Zu zwei Bemerkungen Kummers. Nachr. Akad. d. Wiss. Göttingen, Math. Phys. Kl., II, 1964, 51-62. Reprinted in Gesammelte Abhandlungen (edited by K. Chandrasekharan and H. Maas), Vol. III, 436-442. Springer-Verlag, Berlin, 1966.
%H A092605 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. 502.
%H A092605 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A092605 Equals Sum_{k>=0} (-1)^k/(2^k * k!) = Sum_{k>=0} (-1)^k/A000165(k). - _Amiram Eldar_, Aug 15 2020
%F A092605 From _Peter Bala_, Jan 16 2022; (Start)
%F A092605 Equals 16*Sum_{n >= 0} (-1)^n*n^2/((4*n^2 - 1)*(4*n^2 - 9)*(2^n)*n!).
%F A092605 Equals 8*Sum_{n >= 0} (-1)^n/(p(n)*p(n+1)*(2^n)*n!), where p(n) = 4*n^2 + 8*n + 1.
%F A092605 Equals 48*Sum_{n >= 0} (-1)^n/(q(n)*q(n+1)*(2^n)*n!), where q(n) = 8*n^3 + 36*n^2 + 34*n + 1. (End)
%F A092605 Equals i^(i/Pi), where i denotes the imaginary unit. - _Stefano Spezia_, Mar 01 2025
%F A092605 Equals 1 - A290506. - _Amiram Eldar_, Apr 22 2025
%e A092605 0.6065306597126334...
%t A092605 RealDigits[E^-(1/2),10,120][[1]] (* _Harvey P. Dale_, Jul 23 2012 *)
%o A092605 (PARI) exp(-.5) \\ _Charles R Greathouse IV_, Oct 02 2022
%Y A092605 Cf. A000165, A001113, A019774, A068985, A290506.
%K A092605 cons,nonn
%O A092605 0,1
%A A092605 _Mohammad K. Azarian_, Apr 22 2004