A085068 Number of steps >= 1 for iteration of map x -> (4/3)*ceiling(x) to reach an integer when started at n, or -1 if no such integer is ever reached.
1, 3, 2, 1, 2, 9, 1, 8, 3, 1, 7, 2, 1, 2, 6, 1, 3, 4, 1, 5, 2, 1, 2, 3, 1, 6, 4, 1, 3, 2, 1, 2, 4, 1, 5, 3, 1, 4, 2, 1, 2, 4, 1, 3, 8, 1, 4, 2, 1, 2, 3, 1, 4, 7, 1, 3, 2, 1, 2, 7, 1, 4, 3, 1, 9, 2, 1, 2, 6, 1, 3, 6, 1, 5, 2, 1, 2, 3, 1, 6, 5, 1, 3, 2, 1, 2, 8, 1, 5, 3, 1, 5, 2, 1, 2, 5, 1, 3, 4, 1, 6
Offset: 0
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Programs
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Maple
f := x->(4/3)*ceil(x); g := proc(n) local t1,c; global f; t1 := f(n); c := 1; while not type(t1, 'integer') do c := c+1; t1 := f(t1); od; RETURN([c,t1]); end; # second Maple program: a:= proc(n) local i; n; for i do 4/3*ceil(%); if %::integer then return i fi od end: seq(a(n), n=0..100); # Alois P. Heinz, Mar 01 2021 -
Mathematica
f[n_] := Block[{c = 1, k = 4 n/3}, While[ ! IntegerQ@k, c++; k = 4 Ceiling@k/3]; c]; Table[f@n, {n, 0, 104}] (* Robert G. Wilson v *) -
Python
from fractions import Fraction def A085068(n): c, x, m = 1, Fraction(4*n,3), Fraction(4,3) while x.denominator > 1: x = m*x._ceil_() c += 1 return c # Chai Wah Wu, Mar 01 2021
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