OFFSET
1,2
COMMENTS
The constant K(3) 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.H.M. Smeets, Table of n, a(n) for n = 1..20000
A. M. Odlyzko and H. S. Wilf, Functional iteration and the Josephus problem, Glasgow Math. J. 33 (1991), 235-240.
A.H.M. Smeets, 100000 decimal digits
E. T. H. Wang, Phillip C. Washburn, Problem E2604, American Mathematical Monthly, 84 (1977), 821-822.
Eric Weisstein's World of Mathematics, Power Ceilings.
EXAMPLE
1.62227050288476731595695...
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.
(Python)
d, a, n, nmax = 3, 0, 0, 150000
while n < nmax:
n, a = n+1, (a*d)//(d-1)+1
nom, den, pos = a*(d-1)**n, d**n, 0
while pos < 20000:
dig, nom, pos = nom//den, (nom%den)*10, pos+1
print(pos, dig) # A.H.M. Smeets, Jul 05 2019
KEYWORD
nonn,cons
AUTHOR
Ralf Stephan, Apr 23 2003
STATUS
approved