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 A290506 #22 Apr 22 2025 12:20:15
%S A290506 3,9,3,4,6,9,3,4,0,2,8,7,3,6,6,5,7,6,3,9,6,2,0,0,4,6,5,0,0,8,8,1,9,5,
%T A290506 4,6,5,5,8,0,8,1,8,6,4,5,1,2,8,1,3,0,4,4,3,1,7,1,0,7,8,4,1,2,6,4,9,4,
%U A290506 3,4,8,0,5,8,6,2,5,1,5,7,6,0,0,1,3,5,2,3,8,8,4,9,2,0,1,0,5,4,3,9,7,3,5,7,6
%N A290506 Decimal expansion of 1 - 1/e^(1/2).
%C A290506 The amount of time that a customer has to wait for his order at some restaurant is a random variable having an exponential distribution with a mean of x minutes. The probability that the waiting time will be x/2 minutes or less is 1 - 1/e^(1/2).
%C A290506 Siegel's conjecture: this constant gives the density of irregular primes among all the primes (see Ribenboim and Siegel). - _Stefano Spezia_, Apr 22 2025
%D A290506 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 225.
%D A290506 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.
%F A290506 Equals Integral_{x = 0..1/2} exp(-x) dx.
%F A290506 From _Amiram Eldar_, Aug 24 2020: (Start)
%F A290506 Equals Sum_{k>=1} (-1)^(k+1)/(2^k * k!).
%F A290506 Equals 1 - A092605. (End)
%e A290506 0.3934693402873665763962004650088195465580818645128130443171078412649434...
%t A290506 RealDigits[N[1 - 1/E^(1/2), 105]][[1]]
%o A290506 (Magma) SetDefaultRealField(RealField(105)); n:=1-Exp(-1)^(1/2); Reverse(Intseq(Floor(10^105*n)));
%o A290506 (PARI) 1-exp(-1)^(1/2)
%Y A290506 Cf. A092605.
%K A290506 nonn,cons
%O A290506 0,1
%A A290506 _Arkadiusz Wesolowski_, Aug 04 2017