|
Search: id:A087666
|
|
|
| A087666 |
|
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. |
|
+0
8
|
|
| 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; listen)
|
|
|
OFFSET
|
6,2
|
|
|
COMMENT
|
It is conjectured that an integer is always reached if the initial value n/3 is >= 2.
|
|
LINKS
|
J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.
|
|
MAPLE
|
(Gives right answer as long as answer is < M. This is better than the Mma 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 njas)
|
|
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)
|
|
PROGRAM
|
(PARI) a(n)=if(n<0, 0, c=n/3; x=0; while(frac(c)>0, c=c*floor(c); x++); x)
|
|
CROSSREFS
|
Cf. A083863 (integer reached), A086336 and A087663 (records), A057016, A087710, A088706 (inverse).
Sequence in context: A086798 A131099 A098800 this_sequence A061353 A016653 A096088
Adjacent sequences: A087663 A087664 A087665 this_sequence A087667 A087668 A087669
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
njas, Sep 27 2003
|
|
EXTENSIONS
|
More terms and PARI program from Benoit Cloitre, Sep 29 2003
|
|
|
Search completed in 0.002 seconds
|
