cp's OEIS Frontend

A090529 a(n) is the smallest positive m such that n <= m!.

%I A090529 #20 Apr 06 2022 06:04:25
%S A090529 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,
%T A090529 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,
%U A090529 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
%N A090529 a(n) is the smallest positive m such that n <= m!.
%C A090529 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 such 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.
%H A090529 Reinhard Zumkeller, <a href="/A090529/b090529.txt">Table of n, a(n) for n = 0..10000</a>,
%H A090529 Yi Yuan and Zhang Wenpeng, <a href="http://www.gallup.unm.edu/~smarandache/S-analogue-f.pdf">On the Mean Value of the Analogue of Smarandache Function</a>.
%H A090529 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A090529 a(n+1) = A084558(n) + 1. - _Reinhard Zumkeller_, Jan 05 2014
%e A090529 a(4)=3 because 2! < 4 <= 3!;
%e A090529 a(24)=4 because 3! < 24 <= 4!.
%p A090529 A090529 := proc(n)
%p A090529     local a;
%p A090529     for a from 1 do
%p A090529         if a! >= n then
%p A090529             return a;
%p A090529         end if;
%p A090529     end do:
%p A090529 end proc:
%p A090529 seq(A090529(n),n=0..100) ; # _R. J. Mathar_, Apr 06 2022
%t A090529 Array[Block[{m = 1}, While[# > m!, m++]; m] &, 105, 0] (* _Michael De Vlieger_, Nov 18 2017 *)
%t A090529 With[{f=Table[{m,m!},{m,10}]},Table[Select[f,#[[2]]>=n&][[1]],{n,0,110}]][[All,1]] (* _Harvey P. Dale_, Jan 01 2020 *)
%o A090529 (PARI) a(n)=if(n<0,0,p=1;while(p!<n,p++);p)
%o A090529 (PARI) A090529(n)=for(m=1,n,m!<n || return(m))  \\ _M. F. Hasler_, Jan 16 2013
%o A090529 (Haskell)
%o A090529 a090529 n = a090529_list !! n
%o A090529 a090529_list = f 1 1 0 where
%o A090529   f w v u = if u <= w then v : f w v (u+1) else v' : f (w*v') v' (u+1)
%o A090529             where v' = v + 1
%o A090529 -- _Reinhard Zumkeller_, Jan 05 2014
%Y A090529 Cf. A084558, A000142.
%K A090529 nonn
%O A090529 0,3
%A A090529 _Amarnath Murthy_, Dec 07 2003
%E A090529 Better description and more terms from Zhang Wenpeng (wpzhang(AT)nwu.edu.cn), Mar 29 2004