A086283 a(1)=1, a(2)=1 and, for n>2, a(n) is the smallest positive integer such that the sequence of second order absolute difference is the sequence of positive integers {1,2,3,4,...}.

1, 1, 2, 5, 5, 1, 10, 7, 17, 15, 4, 3, 15, 15, 2, 29, 17, 45, 34, 5, 15, 45, 36, 5, 13, 45, 38, 5, 11, 45, 40, 5, 1, 37, 34, 71, 69, 31, 30, 69, 69, 29, 110, 71, 153, 27, 108, 73, 155, 25, 106, 75, 157, 23, 104, 77, 159, 21, 102, 79, 161, 19, 100, 81, 163, 17, 98, 83, 1, 15, 98

Offset

1,3

Comments

A085059 is the smallest positive sequence such that the first order absolute difference is {1,2,3,4,...}. Other related sequences may be found by searching for the words "absolute difference" with the "Lookup" facility.

Links

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

Example

For the initial terms, no smaller positive terms work than
Sequence {a(n)}: 1,1,2,5,5,1,10,7,17,15,4,3,...
First absolute difference: 0,1,3,0,4,9,3,10,2,11,1,...
Second absolute difference: 1,2,3,4,5,6,7,8,9,10,...

Prog

(Haskell)
a086283 n = x086283_list !! (n-1)
a086283_list = 1 : 1 : f 1 0 [1..] where
   f x y (z:zs) = u : f u (abs $ x - u) zs where
     u = minimum [if v < x then x - v else x + v |
                  v <- if y < z then [y + z] else [y + z, y - z]]
-- Reinhard Zumkeller, Oct 17 2014

Crossrefs

Cf. A085059.

Cf. A008344 (absolute differences).

Sequence in context: A320428 A340422 A145428 * A153759 A269992 A146100

Adjacent sequences: A086280 A086281 A086282 * A086284 A086285 A086286

Keyword

nonn

Author

John W. Layman, Aug 28 2003

Status

approved