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

1,2

Links

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

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

Example

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.

Mathematica

next[{a_, b_}]:=Module[{c=a+1}, {c, If[b<c, b*c, Floor[b/c]]}]; Transpose[ NestList[next, {1, 1}, 65]][[2]] (* Harvey P. Dale, Oct 06 2011 *)

Prog

(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

Crossrefs

Cf. A003462, A076041, A076042, A046901.

Sequence in context: A265416 A199953 A364682 * A280580 A288872 A329207

Adjacent sequences: A076036 A076037 A076038 * A076040 A076041 A076042

Keyword

easy,nice,nonn,look

Author

Amarnath Murthy, Oct 29 2002

Extensions

More terms from David Wasserman, Mar 13 2005

Status

approved