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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:
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 *)
PROG
(Python3)
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
CROSSREFS
Sequence in context: A349930 A274512 A175947 * A265027 A079587 A237881
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 11 2003
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)