A370563 - OEIS

%I #10 May 12 2024 11:25:46

%S 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,

%T 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,

%U 3,3,3,9,7,6,5,6,6,3,0,1,9,0,3,1,6,3

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

%H J. Uspensky, <a href="https://archive.org/details/in.ernet.dli.2015.263184/page/n283/mode/2up">Introduction to Mathematical Probability (1937), 277-278</a>.

%F Equals e*(e-2)*(4 +(e-2)*e)/2.

%e 6.104002341363754151667232902275147659559194262...

%t u=N[E^(E - 2)*(4 + (E - 2)*E)/2, 100]; First[RealDigits[u]]

%t N[Mean[Table[Length[NestWhileList[# + RandomReal[1] &, 0, #1 < E &]] - 1, 10^5]]] (* sample mean *)  (* _Peter J. C. Moses_, Apr 30 2024 *)

%Y Cf. A089087, A090142.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, May 01 2024