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 A083286 #61 Jun 19 2025 14:40:44
%S A083286 1,6,2,2,2,7,0,5,0,2,8,8,4,7,6,7,3,1,5,9,5,6,9,5,0,9,8,2,8,9,9,3,2,4,
%T A083286 1,1,3,0,6,6,1,0,5,5,6,2,3,1,3,0,3,7,4,3,2,1,8,5,4,4,3,3,8,7,3,7,8,4,
%U A083286 3,3,9,9,9,7,2,7,4,8,4,4,7,6,3,8,3,6,1,6,5,3,9,8,3,3,2,3,3,4,1,1,0,0
%N A083286 Decimal expansion of K(3), a constant related to the Josephus problem.
%C A083286 The constant K(3) is related to the Josephus problem with q=3 and the computation of A054995.
%C A083286 The number also occurs in Washburn's solution cited in References. Regarding Washburn's limit more generally (with x in place of 3/2) results in a disconnected function as plotted by the Mathematica program below. - _Clark Kimberling_, Oct 24 2012
%D A083286 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Sections 2.13 and 2.30.1, pp. 131, 196.
%H A083286 A.H.M. Smeets, <a href="/A083286/b083286.txt">Table of n, a(n) for n = 1..20000</a>
%H A083286 A. M. Odlyzko and H. S. Wilf, <a href="https://doi.org/10.1017/S0017089500008272">Functional iteration and the Josephus problem</a>, Glasgow Math. J. 33 (1991), 235-240.
%H A083286 A.H.M. Smeets, <a href="/A083286/a083286_2.txt">100000 decimal digits</a>.
%H A083286 E. T. H. Wang, Phillip C. Washburn, <a href="http://www.jstor.org/stable/2322068">Problem E2604</a>, American Mathematical Monthly, 84 (1977), 821-822.
%H A083286 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerCeilings.html">Power Ceilings</a>.
%H A083286 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>.
%e A083286 1.62227050288476731595695...
%t A083286 s[x_, 0] := 0; s[x_, n_] := Floor[x*s[x, n - 1]] + 1
%t A083286 c[x_, n_] := ((1/x)^n) s[x, n]
%t A083286 t = N[c[3/2, 800], 120]
%t A083286 RealDigits[t, 10] (* A083286 *)
%t A083286 (* Display of the surroundings of 3/2 *)
%t A083286 Plot[N[c[x, 20]], {x, 1, 3}]
%t A083286 (* _Clark Kimberling_, Oct 24 2012 *)
%o A083286 (PARI) p=1; N=10^4; for(n=1, N, p=ceil(3/2*p)); c=(p/(3/2)^N)+0.
%o A083286 (Python)
%o A083286 d, a, n, nmax = 3, 0, 0, 150000
%o A083286 while n < nmax:
%o A083286 n, a = n+1, (a*d)//(d-1)+1
%o A083286 nom, den, pos = a*(d-1)**n, d**n, 0
%o A083286 while pos < 20000:
%o A083286 dig, nom, pos = nom//den, (nom%den)*10, pos+1
%o A083286 print(pos,dig) # _A.H.M. Smeets_, Jul 05 2019
%Y A083286 Cf. A054995, A083287.
%K A083286 nonn,cons
%O A083286 1,2
%A A083286 _Ralf Stephan_, Apr 23 2003