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A090529
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a(n) = smallest m such that n <= m!.
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2
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1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Define f(n,k) = floor[n/k]. Let f(n,2)= n_2, f(n_2,3) = n_3, ...f(n_r, r+1) = n_(r+1). a(n) = least value of r so that n_r = 0. E.g. a(10) = 4, 10 ->10/1 ->10 ->10/2 ->5 ->5/3 ->1 ->1/4 ->0 in four steps.
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LINKS
| Yi Yuan and Zhang Wenpeng, On the Mean Value of the Analogue of Smarandache Function.
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EXAMPLE
| a(4)=3 because 2!< 4 <=3!, a(24)=4 because 3!< 24 <=4!.
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PROG
| (PARI) a(n)=if(n<0, 0, p=1; while(p!<n, p++); p)
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CROSSREFS
| Sequence in context: A093493 A087162 A046925 * A155934 A130822 A194220
Adjacent sequences: A090526 A090527 A090528 * A090530 A090531 A090532
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 07 2003
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EXTENSIONS
| Better description and more terms from Zhang Wenpeng (wpzhang(AT)nwu.edu.cn), Mar 29 2004
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