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Search: id:A087669
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| A087669 |
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Consider recurrence b(0) = (2n+1)/n, b(n) = b(n-1)*floor(b(n-1)); sequence gives number of steps to reach an integer, or -1 if no integer is ever reached. |
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+0
2
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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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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It is conjectured that an integer is always reached if the initial value is >= 2.
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LINKS
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J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.
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MAPLE
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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
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Cf. A087670 (integer reached), A087666.
Adjacent sequences: A087666 A087667 A087668 this_sequence A087670 A087671 A087672
Sequence in context: A076243 A140061 A061313 this_sequence A053087 A062327 A075491
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KEYWORD
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nonn,more
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AUTHOR
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njas, Sep 27 2003
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EXTENSIONS
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I would also like to get the sequences giving the records here and their locations (analogous to A086336 and A087663 for A087666). - njas
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 12 2007
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