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A087666
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Consider recurrence b(0) = n/3, b(k+1) = b(k)*floor(b(k)); a(n) is the least k such that b(k) is an integer, or -1 if no integer is ever reached.
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9
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0, 3, 4, 0, 1, 1, 0, 3, 2, 0, 3, 7, 0, 1, 1, 0, 2, 3, 0, 2, 2, 0, 1, 1, 0, 5, 5, 0, 5, 6, 0, 1, 1, 0, 9, 2, 0, 8, 3, 0, 1, 1, 0, 2, 5, 0, 2, 2, 0, 1, 1, 0, 3, 3, 0, 6, 3, 0, 1, 1, 0, 4, 2, 0, 6, 4, 0, 1, 1, 0, 2, 4, 0, 2, 2, 0, 1, 1, 0, 6, 4, 0, 3, 6, 0, 1, 1, 0, 3, 2, 0, 3, 4, 0, 1, 1, 0, 2, 3, 0, 2, 2, 0, 1, 1, 0, 4, 7, 0, 6, 6, 0, 1, 1, 0, 5, 2, 0, 4, 3, 0, 1, 1, 0, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 6,2
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COMMENTS
| It is conjectured that an integer is always reached if the initial value n/3 is >= 2.
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LINKS
| J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.
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MAPLE
| (Gives right answer as long as answer is < M. This is better than the Mathematica or PARI programs): M := 50; f := proc(n) local c, k, tn, tf; global M; k := n/3; c := 0; while whattype(k) <> 'integer' do tn := floor(k); tf := k-tn; tn := tn mod 3^50; k := tn*(tn+tf); c := c+1; od: c; end; (from N. J. A. Sloane (njas(AT)research.att.com))
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MATHEMATICA
| f[n_] := If[ Mod[3n, 3] == 0, 0, Length[ NestWhileList[ #1*Floor[ #1] &, n, !IntegerQ[ #2] &, 2]] - 1]; Table[f[n/3], {n, 6, 120}] (from Robert G. Wilson v)
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PROG
| (PARI) a(n)=if(n<0, 0, c=n/3; x=0; while(frac(c)>0, c=c*floor(c); x++); x)
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CROSSREFS
| Cf. A083863 (integer reached), A086336 and A087663 (records), A057016, A087710, A088706 (inverse).
Sequence in context: A155061 A131099 A098800 * A061353 A016653 A096088
Adjacent sequences: A087663 A087664 A087665 * A087667 A087668 A087669
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Sep 27 2003
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EXTENSIONS
| More terms and PARI program from Benoit Cloitre, Sep 29 2003
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