A092605 - OEIS

A092605

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

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, 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, 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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

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

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

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.

LINKS

Table of n, a(n) for n=0..104.

Michael I. Shamos, A catalog of the real numbers, (2007). See p. 502.

Index entries for transcendental numbers.

FORMULA

Equals Sum_{k>=0} (-1)^k/(2^k * k!) = Sum_{k>=0} (-1)^k/A000165(k). - Amiram Eldar, Aug 15 2020

From Peter Bala, Jan 16 2022; (Start)

Equals 16*Sum_{n >= 0} (-1)^n*n^2/((4*n^2 - 1)*(4*n^2 - 9)*(2^n)*n!).

Equals 8*Sum_{n >= 0} (-1)^n/(p(n)*p(n+1)*(2^n)*n!), where p(n) = 4*n^2 + 8*n + 1.

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)

Equals i^(i/Pi), where i denotes the imaginary unit. - Stefano Spezia, Mar 01 2025

Equals 1 - A290506. - Amiram Eldar, Apr 22 2025