A076039 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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