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%I #14 Sep 02 2023 16:58:35
%S 5,4,1,3,2,1,2,3,1,10,4,1,6,2,1,2,9,1,3,3,1,5,2,1,2,5,1,4,8,1,3,2,1,2,
%T 3,1,4,12,1,5,2,1,2,4,1,3,3,1,7,2,1,2,4,1,5,6,1,3,2,1,2,3,1,11,5,1,4,
%U 2,1,2,6,1,3,3,1,4,2,1,2,5,1,6,4,1,3,2,1,2,3,1,6,4,1,5,2,1,2,5,1,3
%N Number of steps for iteration of map x -> (5/3)*ceiling(x) to reach an integer > n when started at n, or -1 if no such integer is ever reached.
%C It is conjectured that an integer is always reached.
%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 c2 := proc(x,y) x*ceil(y); end; r := 5/3; ch := proc(x) local n,y; global r; y := c2(r,x); for n from 1 to 20 do if whattype(y) = 'integer' then RETURN([x,n,y]); else y := c2(r,y); fi; od: RETURN(['NULL','NULL','NULL']); end; [seq(ch(n)[2],n=1..100)];
%o (Python)
%o from fractions import Fraction
%o def A087707(n):
%o x, c = Fraction(n), 0
%o while x.denominator > 1 or x<=n:
%o x = Fraction(5*x.__ceil__(),3)
%o c += 1
%o return c # _Chai Wah Wu_, Sep 02 2023
%Y Cf. A087704, A087705, A087706, A087708, A087709.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Sep 29 2003
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