A076039 Start with 1. Multiply or divide by n accordingly as a(n-1) is smaller or greater than n and then take the integer value (this is to ensure that a(n) > 0 for all n).

1, 2, 6, 1, 5, 30, 4, 32, 3, 30, 2, 24, 1, 14, 210, 13, 221, 12, 228, 11, 231, 10, 230, 9, 225, 8, 216, 7, 203, 6, 186, 5, 165, 4, 140, 3, 111, 2, 78, 1, 41, 1722, 40, 1760, 39, 1794, 38, 1824, 37, 1850, 36, 1872, 35, 1890, 34, 1904, 33, 1914, 32, 1920, 31, 1922, 30, 1920

Offset: 1

Author

Amarnath Murthy, Oct 29 2002

Keywords

• easy
• nice
• nonn
• look

Examples

			a(13) = 1 so a(14) = 14*1 = 14;
14 < 15 so a(15) = 14*15 = 210;
210 > 16 so a(16) = floor(210/16) = 13.
		

Links

• William A. Tedeschi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003462, A076041, A076042, A046901.

Programs

Haskell

a076039 n = a076039_list !! (n-1)
a076039_list = f 1 1 where
   f n x = x' : f (n+1) x' where
           x' = (if x < n then (*) else div) x n
-- Reinhard Zumkeller, Aug 24 2011

Mathematica

next[{a_,b_}]:=Module[{c=a+1},{c,If[bHarvey P. Dale, Oct 06 2011 *)

Formula

a(n) = n*a(n-1) if a(n-1) < n, floor(a(n-1)/n) otherwise.

a(A003462(k)) = 1. For A003462(k) < n <= A003462(k+1), if n-A003462(k) is odd, then a(n) = (3*A003462(k)+3-n)/2 and if n-A003462(k) is even, then a(n) = n*a(n-1). - David Wasserman, Mar 13 2005

Extensions

More terms from David Wasserman, Mar 13 2005