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A083514
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Number of steps for iteration of map x -> (4/3)*ceiling(x) to reach an integer > 3n+1 when started at 3n+1, or -1 if no such integer is ever reached.
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1
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3, 2, 8, 7, 2, 3, 5, 2, 6, 3, 2, 5, 4, 2, 3, 4, 2, 4, 3, 2, 4, 9, 2, 3, 5, 2, 6, 3, 2, 5, 5, 2, 3, 6, 2, 5, 3, 2, 7, 4, 2, 3, 4, 2, 4, 3, 2, 4, 5, 2, 3, 6, 2, 5, 3, 2, 8, 8, 2, 3, 7, 2, 7, 3, 2, 6, 4, 2, 3, 4, 2, 4, 3, 2, 4, 7, 2, 3, 8, 2, 8, 3, 2, 6, 6, 2, 3, 5, 2, 8, 3, 2, 5, 4, 2, 3, 4, 2, 4, 3, 2, 4, 6, 2, 3
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OFFSET
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0,1
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COMMENTS
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It is conjectured that an integer is always reached.
Also number of steps for iteration of map x -> (4/3)*floor(x) to reach an integer when started at 3n+4.
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LINKS
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Table of n, a(n) for n=0..104.
J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.
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FORMULA
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a(3n+1)=2.
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MAPLE
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b:= proc(n) local i; n; for i do 4/3*ceil(%);
if %::integer then return i fi od
end:
a:= n-> b(3*n+1):
seq(a(n), n=0..100); # Alois P. Heinz, Mar 01 2021
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PROG
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(PARI) a(n)=if(n<0, 0, c=(3*n+1)*4/3; x=1; while(frac(c)>0, c=4/3*ceil(c); x++); x)
(PARI) a(n)=if(n<0, 0, c=(3*n+4)*4/3; x=1; while(frac(c)>0, c=4/3*floor(c); x++); x)
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CROSSREFS
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Equals A085068(3n+1).
Sequence in context: A092174 A245781 A239803 * A123696 A123500 A074689
Adjacent sequences: A083511 A083512 A083513 * A083515 A083516 A083517
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Benoit Cloitre, Sep 28 2003
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STATUS
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approved
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