A085071 - OEIS

%I #17 Feb 17 2023 07:38:44

%S 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,

%T 148,84,36,68,52,40,56,104,44,148,84,48,120,68,52,72,132,56,104,452,

%U 60,148,84,64,88,120,68,168,404,72,132,100,76,104,452,80,196,148,84,872,116,88

%N Integers reached in A085068.

%H J. C. Lagarias and N. J. A. Sloane, Approximate squaring (<a href="http://neilsloane.com/doc/apsq.pdf">pdf</a>, <a href="http://neilsloane.com/doc/apsq.ps">ps</a>), Experimental Math., 13 (2004), 113-128.

%p a:= proc(n) local i; n; for i do 4/3*ceil(%);

%p       if %::integer then return % fi od

%p     end:

%p seq(a(n), n=0..100);  # _Alois P. Heinz_, Mar 01 2021

%t a[n_] := Module[{k = 4n/3}, While[!IntegerQ[k], k = 4* Ceiling[k]/3]; k];

%t Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Feb 17 2023 *)

%o (Python3)

%o from fractions import Fraction

%o def A085071(n):

%o     c, x = 0, Fraction(n,1)

%o     while x.denominator > 1 or x <= n:

%o         x = Fraction(4*x.__ceil__(),3)

%o         c += 1

%o     return x.numerator # _Chai Wah Wu_, Mar 01 2021

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Aug 11 2003