A089139 Decimal expansion of e^4 - 3*e^3 + 2*e^2 - e/6.

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

Offset: 1

Author

Brian Dunfield (brian.dunfield(AT)sympatico.ca), Dec 05 2003

Keywords

• nonn
• cons
• easy

Comments

Expected number of picks from a uniform [0,1] needed to first exceed a sum of 4.

Examples

			8.66660449003269543722547924837362992189477014843865301170288564321492595275913921...
		

References

• J. V. Uspensky, Introduction to Mathematical Probability, New York: McGraw-Hill, 1937.

Links

• Daniel Mondot, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Uniform Sum Distribution
• Index entries for transcendental numbers

Crossrefs

Cf. A001113, A090142, A090143, A090611, A379601, A381673, A382020, A381843, A382026, A090137, A090138, A089087.

Programs

Mathematica

RealDigits[ E^4 - 3E^3 + 2E^2 - E/6, 10, 111][[1]] (* Robert G. Wilson v, Dec 05 2003 *)

PARI

subst(x^4-3*x^3+2*x^2-x/6, x, exp(1)) \\ Charles R Greathouse IV, Dec 06 2016

Formula

Equals Sum_{k=0..n} (-1)^k * (n-k+1)^k * exp(n-k+1) / k! for n = 3 (Uspensky, 1937, p. 278).

Extensions

Edited and extended by Robert G. Wilson v and Ray Chandler, Dec 07 2003