A085059 a(1) = 1, a(n+1) = a(n)-n if a(n) > n else a(n+1) = a(n) + n.

1, 2, 4, 1, 5, 10, 4, 11, 3, 12, 2, 13, 1, 14, 28, 13, 29, 12, 30, 11, 31, 10, 32, 9, 33, 8, 34, 7, 35, 6, 36, 5, 37, 4, 38, 3, 39, 2, 40, 1, 41, 82, 40, 83, 39, 84, 38, 85, 37, 86, 36, 87, 35, 88, 34, 89, 33, 90, 32, 91, 31, 92, 30, 93, 29, 94, 28, 95, 27, 96, 26, 97, 25, 98, 24, 99

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 27 2003

Keywords

• nonn
• easy
• look

Comments

Let (3^k-1)/2 = r then a((3^k-1)/2) = a(r) = 1 and a(r-1) = r. Geometrical interpretation. The sequence is obtained by the following rule: A point moves on the positive number line with the rule that in every step it has to move one unit more than the previous step and with the aim that it is to be as close to 0 as possible but on the positive side.

Links

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

Crossrefs

Cf. A005132.

Equals 1+A008344(n).

Cf. A046901.

Programs

Haskell

a085059 n = a085059_list !! (n-1)
a085059_list = 1 : f 1 1 where
   f v w = y : f (v + 1) y where
     y = if w > v then w - v else w + v
-- Reinhard Zumkeller, Jan 31 2013

Mathematica

RecurrenceTable[{a[1]==1,a[n+1]==If[a[n]>n,a[n]-n , a[n]+n]}, a[n], {n,80}] (* Harvey P. Dale, May 11 2011 *)

Formula

a(A003462(n)) = 1. - Reinhard Zumkeller, Jan 31 2013

Extensions

More terms from Sam Alexander, Oct 20 2003