A064619 Decimal expansion of sqrt(2*log(2)).

1, 1, 7, 7, 4, 1, 0, 0, 2, 2, 5, 1, 5, 4, 7, 4, 6, 9, 1, 0, 1, 1, 5, 6, 9, 3, 2, 6, 4, 5, 9, 6, 9, 9, 6, 3, 7, 7, 4, 7, 3, 8, 5, 6, 8, 9, 3, 8, 5, 8, 2, 0, 5, 3, 8, 5, 2, 2, 5, 2, 5, 7, 5, 6, 5, 0, 0, 0, 2, 6, 5, 8, 8, 5, 4, 6, 9, 8, 4, 9, 2, 6, 8, 0, 8, 4, 1, 8, 1, 3, 8, 3, 6, 8, 7, 7, 0, 8, 1

Offset: 1

Author

Henrik Johansson (johansson.henrik(AT)home.se), Jun 06 2002

Keywords

• cons
• nonn

Comments

Constant arising from birthday paradox: if the year has n days, the number of people required so that the probability that at least two of them have the same birthday is 1/2 approaches 1.1774100225...*sqrt(n) for large n.

Examples

			1.1774100225...
		

References

• W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, 2nd ed. New York: Wiley, p. 31, 1968.
• B. Barwell, Journal of Recreational Mathematics, Soln. to Prob. 2393: "Matching Birthdays on Mars" 30(1) 71 1999-2000.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Index entries for transcendental numbers

Crossrefs

Cf. A051008.

Programs

Mathematica

RealDigits[Sqrt[2*Log[2]], 10, 50][[1]] (* G. C. Greubel, Sep 23 2017 *)

PARI

default(realprecision, 20080); x=sqrt(2*log(2)); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b064619.txt", n, " ", d)) \\ Harry J. Smith, Sep 20 2009