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Search: id:A072340
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| A072340 |
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Number of steps to reach an integer starting with n/3 and iterating the map x -> x*ceiling(x), or -1 if no integer is ever reached. |
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+0
12
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| 0, 2, 6, 0, 1, 1, 0, 5, 2, 0, 3, 2, 0, 1, 1, 0, 2, 4, 0, 3, 4, 0, 1, 1, 0, 22, 7, 0, 2, 5, 0, 1, 1, 0, 7, 2, 0, 4, 2, 0, 1, 1, 0, 2, 5, 0, 13, 9, 0, 1, 1, 0, 3, 3, 0, 2, 3, 0, 1, 1, 0, 3, 2, 0, 5, 2, 0, 1, 1, 0, 2, 3, 0, 8, 3, 0, 1, 1, 0, 5, 4, 0, 2, 4, 0, 1, 1, 0, 14, 2, 0, 3, 2, 0, 1, 1, 0, 2, 9, 0, 3, 9, 0, 1, 1
(list; graph; listen)
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OFFSET
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3,2
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COMMENT
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We conjecture that an integer is always reached.
The occurrence of the first 1, 2, 3, 4 etc. is at the indices 7, 4, 13, 20, 10, 5, 29, 76, 50, 452, 244, 830, 49, 91, 319, 2639, 5753, 2215, 6151, 7148, 280, 28, 1783 - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 25 2006
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LINKS
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R. J. Mathar, Table of n, a(n) for n = 3..7147
J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.
N. J. A. Sloane, Seven Staggering Sequences.
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MAPLE
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g := proc(x) local M, t1, t2, t3; M := 3^100; t1 := ceil(x) mod M; t2 := x*t1; t3 := numer(t2) mod M; t3/denom(t2); end;
f := proc(n) local t1, c; global g; if type(n, 'integer') then RETURN(0); fi; t1 := g(n); c := 1; while not type(t1, 'integer') do c := c+1; t1 := g(t1); od; RETURN(c); end;
[seq(f(n/3), n=3..120)]; # this gives the correct answer as long as the answer is < 99.
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PROGRAM
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(PARI) A072340(n)={ local(x, s) ; x=n/3 ; s=0 ; while( type(x)!="t_INT", x *= ceil(x) ; s++ ; ) ; return(s) ; } { for(n=3, 10000, print(n, " ", A072340(n)) ; ) ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 25 2006
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CROSSREFS
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Cf. A085276, A085285, A085286, A073524.
Sequence in context: A139062 A122760 A039907 this_sequence A118354 A080730 A016590
Adjacent sequences: A072337 A072338 A072339 this_sequence A072341 A072342 A072343
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KEYWORD
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nonn
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AUTHOR
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njas and J. C. Lagarias, Sep 03 2002
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