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 A083286 Decimal expansion of K(3), a constant related to the Josephus problem. 10
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The constant K(3) = 1.62227050288476731595695... is related to the Josephus problem with q=3 and the computation of A054995. 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 LINKS A. M. Odlyzko and H. S. Wilf, Functional iteration and the Josephus problem, Glasgow Math. J. 33, 235-240, 1991. E. T. H. Wang, Phillip C. Washburn, Problem E2604, American Mathematical Monthly 84 (1977) pp. 821-822. Eric Weisstein's World of Mathematics, Power Ceilings MATHEMATICA s[x_, 0] := 0; s[x_, n_] := Floor[x*s[x, n - 1]] + 1 c[x_, n_] := ((1/x)^n) s[x, n] t = N[c[3/2, 800], 120] RealDigits[t, 10]  (* A083286 *) (* Display of the surroundings of 3/2 *) Plot[N[c[x, 20]], {x, 1, 3}] (* Clark Kimberling, Oct 24 2012 *) PROG (PARI) p=1; N=10^4; for(n=1, N, p=ceil(3/2*p)); c=(p/(3/2)^N)+0. CROSSREFS Cf. A054995, A083287. Sequence in context: A020795 A136710 A276801 * A247818 A172439 A169684 Adjacent sequences:  A083283 A083284 A083285 * A083287 A083288 A083289 KEYWORD nonn,cons AUTHOR Ralf Stephan, Apr 23 2003 STATUS approved

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Last modified September 25 20:53 EDT 2018. Contains 315425 sequences. (Running on oeis4.)