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 A245771 #40 Jun 10 2025 01:12:48
%S A245771 1,7,6,7,9,9,3,7,8,6,1,3,6,1,5,4,0,5,0,4,4,3,6,3,4,4,0,6,7,8,1,1,3,2,
%T A245771 3,3,1,0,7,7,6,8,1,4,3,3,1,3,1,9,5,6,5,1,5,5,7,6,9,8,6,0,5,9,6,2,6,0,
%U A245771 0,0,7,6,4,6,0,6,3,8,7,5,1,4,4,4,4,8,1,6,5,1,6,3,2,5,6,8,2,5,0
%N A245771 Decimal expansion of 'b', an optimal stopping constant associated with the secretary problem when the objective is to maximize the hiree's expected quality.
%D A245771 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15, p. 362.
%H A245771 Steven Finch, <a href="https://arxiv.org/abs/2409.03510">A Deceptively Simple Quadratic Recurrence</a>, arXiv:2409.03510 [math.NT], 2024.
%H A245771 Steven Finch, <a href="https://arxiv.org/abs/2411.16062">Exercises in Iterational Asymptotics</a>, arXiv:2411.16062 [math.NT], 2024. See p. 9.
%H A245771 Steven Finch, <a href="https://arxiv.org/abs/2506.07625">Half-Iterates of x(1+x), sin(x) and exp(x/e)</a>, arXiv:2506.07625 [math.NT], 2025. See p. 4.
%H A245771 Jon E. Schoenfield, <a href="/A245771/a245771.txt">Magma program</a> communicated to J.-F. Alcover.
%H A245771 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SultansDowryProblem.html">Sultan's Dowry Problem</a>.
%H A245771 Wikipedia, <a href="http://en.wikipedia.org/wiki/Secretary_problem">Secretary problem</a>.
%F A245771 Q(0) = 0, Q(n) = (1/2)*(1+Q(n-1)^2), Q(n) ~ 1-2/(n+log(n)+b) when n -> infinity.
%e A245771 1.767993786136154050443634406781132331077681433131956515576986059626...
%t A245771 nmax = 10^10; dn = 10^6; db = 2*10^-16; b0 = p = 3; q = 10/3; b = q - Log[2]; f = Compile[{n, p, q}, (p*((p-5)*p + 8) + n*(n*p + (2*p-5)*p + 2) + q - 5)/((p-5)*p + n*(n + 2*p - 5) + 7)]; For[n = 3, n <= nmax, n++, If[Divisible[n, dn], b0 = b]; r = f[n, p, q]; b = r - Log[n]; p = q; q = r; If[Divisible[n, dn], Print["n = ", n, " b = ", b]; If[Abs[b - b0] < db, Break[]]]]; RealDigits[b] // First
%o A245771 (Magma) // See the link to _Jon E. Schoenfield_'s program.
%Y A245771 Cf. A054404, A242672, A242673, A242674, A243533.
%K A245771 nonn,cons
%O A245771 1,2
%A A245771 _Jean-François Alcover_, Aug 01 2014
%E A245771 Extended to 99 digits using _Jon E. Schoenfield_'s evaluation, Sep 05 2016