A085071 Integers reached in A085068.

0, 4, 4, 4, 8, 84, 8, 84, 20, 12, 84, 20, 16, 24, 84, 20, 40, 56, 24, 84, 36, 28, 40, 56, 32, 148, 84, 36, 68, 52, 40, 56, 104, 44, 148, 84, 48, 120, 68, 52, 72, 132, 56, 104, 452, 60, 148, 84, 64, 88, 120, 68, 168, 404, 72, 132, 100, 76, 104, 452, 80, 196, 148, 84, 872, 116, 88

Offset: 0

Author

N. J. A. Sloane, Aug 11 2003

Keywords

• nonn

Links

• J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.

Programs

Maple

a:= proc(n) local i; n; for i do 4/3*ceil(%);
      if %::integer then return % fi od
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Mar 01 2021

Mathematica

a[n_] := Module[{k = 4n/3}, While[!IntegerQ[k], k = 4* Ceiling[k]/3]; k];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 17 2023 *)

Python3

from fractions import Fraction
def A085071(n):
    c, x = 0, Fraction(n,1)
    while x.denominator > 1 or x <= n:
        x = Fraction(4*x._ceil_(),3)
        c += 1
    return x.numerator # Chai Wah Wu, Mar 01 2021