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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

REFERENCES

E. T. H. Wang, Phillip C. Washburn, Problem E2604, American Mathematical Monthly 84 (1977) pp. 821-822.

LINKS

Table of n, a(n) for n=1..102.

A. M. Odlyzko and H. S. Wilf, Functional iteration and the Josephus problem

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 June 22 12:17 EDT 2017. Contains 288613 sequences.