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, 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, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15

Offset

1,2

Comments

a(n+1) = number of Mancala numbers <= n, see A007952; n occurs A028913(n-1) times consecutively. - Reinhard Zumkeller, Jun 21 2008

a(n) = number of ones <= n in A130747; see also A002491. - Reinhard Zumkeller, Jul 01 2009

Links

R. Zumkeller, Table of n, a(n) for n = 1..10000

Formula

Conjecture: a(n) = sqrt(Pi*n) + O(1)

a(n) = A073047(n) - 1.

Example

If 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.
If 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.

Mathematica

Flatten@Table[First@Position[Rest@FoldList[#1-Mod[#1, #2]&, i, Range[2, i+1]], 0], {i, 30}] (* Birkas Gyorgy, Feb 26 2011 *)

Prog

(PARI) a(n)=if(n<1, 0, s=n; c=1; while(s-s%c>0, s=s-s%c; c++); c)

Crossrefs

Cf. A140060, A140061.

Sequence in context: A071868 A179390 A237819 * A139789 A366033 A000720

Adjacent sequences: A082444 A082445 A082446 * A082448 A082449 A082450

Keyword

nonn

Author

Benoit Cloitre, Apr 25 2003

Status

approved