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

1,2

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

Formula

a(A003462(n)) = 1. - 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 *)

Prog

(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

Crossrefs

Cf. A005132.

Equals 1+A008344(n).

Cf. A046901.

Sequence in context: A283739 A080427 A118906 * A336164 A379572 A181336

Adjacent sequences: A085056 A085057 A085058 * A085060 A085061 A085062

Keyword

nonn,easy,look

Author

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

Extensions

More terms from Sam Alexander, Oct 20 2003

Status

approved