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A087669
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The smallest index m such that b(m) is an integer, where b(0)=(2n+1)/n and b(k+1)=b(k)*floor(b(k)) for k>=0.
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4
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0, 1, 3, 2, 5, 4, 5, 2, 4, 9, 19, 7, 16, 7, 8, 3, 27, 9, 5, 25, 10, 11, 32, 4, 13, 4, 17, 6, 17, 6, 78, 3, 23, 47, 13, 6, 4, 6, 27, 9, 20, 6, 4, 17, 9, 28, 106, 4, 24, 28, 37, 20, 27, 10, 12, 13, 7, 83, 108, 10, 16, 9, 6, 3, 10, 11, 15, 8, 11, 6, 156, 15, 38, 46, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| It is conjectured that an integer is always reached if the initial value 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.
Max Alekseyev, Table of n, a(n) for n = 1..10000
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MAPLE
| A087669 := proc(n) local b, stps ; stps := 0 ; b := (2*n+1)/n ; while not type(b, 'integer') do b := b*floor(b) ; stps := stps+1 ; od ; RETURN(stps) ; end: for n from 1 to 100 do print(n, A087669(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 12 2007
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CROSSREFS
| The records and their indices are given by A192230 and A192229.
Cf. A087670 (integer reached), A087666.
Sequence in context: A076243 A140061 A061313 * A053087 A062327 A075491
Adjacent sequences: A087666 A087667 A087668 * A087670 A087671 A087672
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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 from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 12 2007
Terms a(23) onward from Max Alekseyev (maxale(AT)gmail.com), Jun 25 2011
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