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A087705 First integer > n reached under iteration of map x -> (5/3)*floor(x) when started at n, or -1 if no such integer is ever reached.

%I A087705 #21 Sep 02 2023 04:36:38
%S A087705 5,5,10,35,10,30,35,15,905,30,20,35,105,25,905,210,30,85,55,35,60,105,
%T A087705 40,2410,905,45,210,80,50,85,405,55,155,160,60,280,105,65,110,2410,70,
%U A087705 905,335,75,210,130,80,135,230,85,660,405,90,1160,155,95,160,2085,100
%N A087705 First integer > n reached under iteration of map x -> (5/3)*floor(x) when started at n, or -1 if no such integer is ever reached.
%C A087705 It is conjectured that an integer is always reached.
%H A087705 Robert Israel, <a href="/A087705/b087705.txt">Table of n, a(n) for n = 2..10000</a>
%H A087705 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 A087705 f2 := proc(x,y) x*floor(y); end; r := 5/3; h := proc(x) local n,y; global r; y := f2(r,x); for n from 1 to 20 do if whattype(y) = 'integer' then RETURN([x,n,y]); else y := f2(r,y); fi; od: RETURN(['NULL','NULL','NULL']); end; [seq(h(n)[3],n=2..60)];
%o A087705 (Python)
%o A087705 from fractions import Fraction
%o A087705 def A087705(n):
%o A087705     x = Fraction(n,1)
%o A087705     while x.denominator > 1 or x<=n:
%o A087705         x = Fraction(5*x.__floor__(),3)
%o A087705     return int(x) # _Chai Wah Wu_, Sep 01 2023
%Y A087705 Cf. A087704, A087706.
%K A087705 nonn
%O A087705 2,1
%A A087705 _N. J. A. Sloane_, Sep 29 2003