A290506 Decimal expansion of 1 - 1/e^(1/2).

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, 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, 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

Offset: 0

Author

Arkadiusz Wesolowski, Aug 04 2017

Keywords

• nonn
• cons

Comments

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).

Siegel's conjecture: this constant gives the density of irregular primes among all the primes (see Ribenboim and Siegel). - Stefano Spezia, Apr 22 2025

Examples

			0.3934693402873665763962004650088195465580818645128130443171078412649434...
		

References

• Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 225.
• 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.

Crossrefs

Cf. A092605.

Programs

Magma

SetDefaultRealField(RealField(105)); n:=1-Exp(-1)^(1/2); Reverse(Intseq(Floor(10^105*n)));

Mathematica

RealDigits[N[1 - 1/E^(1/2), 105]][[1]]

PARI

1-exp(-1)^(1/2)

Formula

Equals Integral_{x = 0..1/2} exp(-x) dx.

From Amiram Eldar, Aug 24 2020: (Start)

Equals Sum_{k>=1} (-1)^(k+1)/(2^k * k!).

Equals 1 - A092605. (End)