A370563 Decimal expansion of expected number of trials needed for the sum of uniform random variables from the interval [0,1] to exceed e.

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

Offset

1,1

Links

Table of n, a(n) for n=1..86.

J. Uspensky, Introduction to Mathematical Probability (1937), 277-278.

Formula

Equals e^(e-2)*(4 +(e-2)*e)/2.

Example

6.104002341363754151667232902275147659559194262...

Mathematica

u=N[E^(E - 2)*(4 + (E - 2)*E)/2, 100]; First[RealDigits[u]]
N[Mean[Table[Length[NestWhileList[# + RandomReal[1] &, 0, #1 < E &]] - 1, 10^5]]] (* sample mean *)  (* Peter J. C. Moses, Apr 30 2024 *)

Prog

(PARI) exp(exp(1)-2)*(4 +(exp(1)-2)*exp(1))/2 \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A089087, A090142.

Sequence in context: A011221 A347237 A090203 * A120113 A074395 A355415

Adjacent sequences: A370560 A370561 A370562 * A370564 A370565 A370566

Keyword

nonn,cons

Author

Clark Kimberling, May 01 2024

Status

approved