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Search: id:A085068
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| A085068 |
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Number of steps for iteration of map x -> (4/3)*ceiling(x) to reach an integer > n when started at n, or -1 if no such integer is ever reached. |
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+0
8
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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It is conjectured that an integer is always reached.
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LINKS
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J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.
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MAPLE
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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;
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A085058, A085071, A085328, A085330, A083514.
Adjacent sequences: A085065 A085066 A085067 this_sequence A085069 A085070 A085071
Sequence in context: A048984 A136531 A127318 this_sequence A079587 A112745 A036585
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KEYWORD
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nonn
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AUTHOR
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njas, Aug 11 2003
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