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 A083514 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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. LINKS 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. FORMULA a(3n+1)=2. MAPLE 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 PROG (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) CROSSREFS Equals A085068(3n+1). Sequence in context: A092174 A245781 A239803 * A123696 A123500 A074689 Adjacent sequences: A083511 A083512 A083513 * A083515 A083516 A083517 KEYWORD nonn,easy AUTHOR Benoit Cloitre, Sep 28 2003 STATUS approved

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Last modified April 20 09:57 EDT 2024. Contains 371806 sequences. (Running on oeis4.)