login
This site is supported by donations to The OEIS Foundation.

 

Logo


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!. 50
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<p else a007623(int(n/p), p+1)*10 + n%p

def a(n): return 0 if n==0 else len(str(a007623(n)))

print [a(n) for n in xrange(101)] # Indranil Ghosh, Jun 24 2017

(PARI) a(n)={my(m=0); while(n\=m++, ); m-1} \\ R. J. Cano, Apr 09 2018

CROSSREFS

A dual to A090529.

Cf. A084555-A084557.

Cf. A001069, A010096.

Cf. A000142, A001563, A055089, A060130, A111095, A211664, A211670, A108731, A212598, A220656, A220657, A220658, A220659, A231716, A235224, A257510.

Sequence in context: A235224 A069624 A092139 * A163291 A156875 A066339

Adjacent sequences:  A084555 A084556 A084557 * A084559 A084560 A084561

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 23 2003

EXTENSIONS

Name clarified by Antti Karttunen, Apr 27 2015

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified July 22 17:31 EDT 2018. Contains 312914 sequences. (Running on oeis4.)