|
|
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.
|
|
8
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
It is conjectured that an integer is always reached.
|
|
LINKS
|
J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.
|
|
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:
|
|
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 *)
|
|
PROG
|
(Python3)
from fractions import Fraction
c, x, m = 1, Fraction(4*n, 3), Fraction(4, 3)
while x.denominator > 1:
x = m*x.__ceil__()
c += 1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|