This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370563 #10 May 12 2024 11:25:46 %S A370563 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 A370563 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 A370563 3,3,3,9,7,6,5,6,6,3,0,1,9,0,3,1,6,3 %N A370563 Decimal expansion of expected number of trials needed for the sum of uniform random variables from the interval [0,1] to exceed e. %H A370563 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 A370563 Equals e*(e-2)*(4 +(e-2)*e)/2. %e A370563 6.104002341363754151667232902275147659559194262... %t A370563 u=N[E^(E - 2)*(4 + (E - 2)*E)/2, 100]; First[RealDigits[u]] %t A370563 N[Mean[Table[Length[NestWhileList[# + RandomReal[1] &, 0, #1 < E &]] - 1, 10^5]]] (* sample mean *) (* _Peter J. C. Moses_, Apr 30 2024 *) %Y A370563 Cf. A089087, A090142. %K A370563 nonn,cons %O A370563 1,1 %A A370563 _Clark Kimberling_, May 01 2024