This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A084558 a(0) = 0; for n >= 1: a(n) = largest m such that n >= m!. 52
 0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For n >= 1, a(n) = the number of significant digits in n's factorial base representation (A007623). After zero, which occurs once, each n occurs A001563(n) times. Number of iterations (...f_4(f_3(f_2(n))))...) such that the result is < 1, where f_j(x):=x/j. - Hieronymus Fischer, Apr 30 2012 For n > 0: a(n) = length of row n in table A108731. - Reinhard Zumkeller, Jan 05 2014 REFERENCES F. Smarandache, "f-Inferior and f-Superior Functions - Generalization of Floor Functions", Arizona State University, Special Collections. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 Yi Yuan and Zhang Wenpeng, On the Mean Value of the Analogue of Smarandache Function, Smarandache Notions J., Vol. 15. FORMULA From Hieronymus Fischer, Apr 30 2012: (Start) a(n!) = a((n-1)!))+1, for n>1. G.f.: 1/(1-x)*Sum_{k>=1} x^(k!). The explicit first terms of the g.f. are: (x+x^2+x^6+x^24+x^120+x^720...)/(1-x). (End) Other identities: For all n >= 0, a(n) = A090529(n+1) - 1. - Reinhard Zumkeller, Jan 05 2014 For all n >= 1, a(n) = A060130(n) + A257510(n). - Antti Karttunen, Apr 27 2015 EXAMPLE a(4) = 2 because 2! <= 4 < 3!. MAPLE 0, seq(m\$(m*m!), m=1..5); # Robert Israel, Apr 27 2015 MATHEMATICA Table[m = 1; While[m! <= n, m++]; m - 1, {n, 0, 104}] (* Jayanta Basu, May 24 2013 *) PROG (Haskell) a084558 n = a090529 (n + 1) - 1  -- Reinhard Zumkeller, Jan 05 2014 (Python) def a007623(n, p=2): return n if n

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 22 11:56 EST 2019. Contains 319363 sequences. (Running on oeis4.)