cp's OEIS Frontend

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.

A348913 Number of N(0,1) variables needed for a 1/2 chance that their maximum exceeds the maximum of n N(1,1) variables.

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%I A348913 #6 Nov 19 2021 07:58:27
%S A348913 4,11,19,29,40,52,64,78,92,106,122,137,154,171,188,205,224,242,261,
%T A348913 280,300,320,340,360,381,402,424,446,468,490,512,535,558,581,605,629,
%U A348913 652,677,701,726,750,775,801,826,852,877,903,929,956,982,1009
%N A348913 Number of N(0,1) variables needed for a 1/2 chance that their maximum exceeds the maximum of n N(1,1) variables.
%C A348913 The above data has only 51 entries because the Mathematica code below would give numerically unstable results for the integrals with n>51.
%H A348913 Matt Frank, <a href="https://stats.stackexchange.com/questions/550015/numerical-superiority-necessary-to-beat-in-l-infty-a-population-one-standard/550799">Answer to "Numerical superiority necessary to beat in L^oo a population one standard deviation ahead"</a>, on CrossValidated (aka stats.stackexchange.com)
%e A348913 For n = 2, a(2) = 11 because if X_i are standard normal variables, and Y_j are normal variables with mean and variance 1, then P[max(X_1, ... X_10) > max(Y_1, Y_2)] = 49% but P[max(X_1, ... X_11) > max(Y_1, Y_2)] = 51%.
%t A348913 cdf[x_] := CDF[NormalDistribution[], x];
%t A348913 prob[m_] := NIntegrate[D[cdf[x]^m, x] cdf[x - 1]^n , {x, -Infinity, Infinity}]
%t A348913 Table[FindArgMin[(prob[m] - 1/2)^2, {m, n^1.75}] // Ceiling, {n, 51}]
%K A348913 nonn,more
%O A348913 1,1
%A A348913 _Matt Frank_, Nov 03 2021