cp's OEIS Frontend

A082447 a(n) = the number k such that s(k)=0 where s(0)=n and s(i)=s(i-1)-(s(i-1) modulo (i+1)).

%I A082447 #41 Aug 03 2025 04:44:58
%S A082447 1,2,2,3,3,4,4,4,4,5,5,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,10,
%T A082447 10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,
%U A082447 13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15
%N A082447 a(n) = the number k such that s(k)=0 where s(0)=n and s(i)=s(i-1)-(s(i-1) modulo (i+1)).
%C A082447 a(n+1) = number of Mancala numbers <= n, see A007952; n occurs A028913(n-1) times consecutively. - _Reinhard Zumkeller_, Jun 21 2008
%C A082447 a(n) = number of ones <= n in A130747; see also A002491. - _Reinhard Zumkeller_, Jul 01 2009
%H A082447 Reinhard Zumkeller, <a href="/A082447/b082447.txt">Table of n, a(n) for n = 1..10000</a>
%F A082447 Conjecture: a(n) = sqrt(Pi*n) + O(1)
%F A082447 a(n) = A073047(n) - 1.
%e A082447 For n=4, s(0)=4, 4 ->4-4 mod 1=4 ->4-4 mod 2=4 ->4-4 mod 3=3 ->3-3 mod 4=0, hence s(4)=0 and a(4)=4.
%e A082447 For n=6, s(0)=6, s(1)=6-6 mod 2=6, s(2)=6-6 mod 3=6, s(3)=6-6 mod 4=6-2=4, s(4)=4-4 mod 5=0, hence a(6)=4.
%t A082447 Flatten@Table[First@Position[Rest@FoldList[#1-Mod[#1,#2]&,i,Range[2,i+1]],0], {i,30}] (* _Birkas Gyorgy_, Feb 26 2011 *)
%o A082447 (PARI) a(n)=if(n<1, 0, s=n; c=1; while(s-s%c>0, s=s-s%c; c++); c--) \\ corrected by _Dan Dima_, Jan 18 2025
%Y A082447 Cf. A073047, A140060, A140061.
%K A082447 nonn
%O A082447 1,2
%A A082447 _Benoit Cloitre_, Apr 25 2003
%E A082447 Name corrected by _Dan Dima_, Jan 18 2025