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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,...}. 3

%I

%S 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,

%T 5,11,45,40,5,1,37,34,71,69,31,30,69,69,29,110,71,153,27,108,73,155,

%U 25,106,75,157,23,104,77,159,21,102,79,161,19,100,81,163,17,98,83,1,15,98

%N 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,...}.

%C 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.

%H Reinhard Zumkeller, <a href="/A086283/b086283.txt">Table of n, a(n) for n = 1..10000</a>

%e For the initial terms, no smaller positive terms work than

%e Sequence {a(n)}: 1,1,2,5,5,1,10,7,17,15,4,3,...

%e First absolute difference: 0,1,3,0,4,9,3,10,2,11,1,...

%e Second absolute difference: 1,2,3,4,5,6,7,8,9,10,...

%o (Haskell)

%o a086283 n = x086283_list !! (n-1)

%o a086283_list = 1 : 1 : f 1 0 [1..] where

%o f x y (z:zs) = u : f u (abs $ x - u) zs where

%o u = minimum [if v < x then x - v else x + v |

%o v <- if y < z then [y + z] else [y + z, y - z]]

%o -- _Reinhard Zumkeller_, Oct 17 2014

%Y Cf. A085059.

%Y Cf. A008344 (absolute differences).

%K nonn

%O 1,3

%A _John W. Layman_, Aug 28 2003

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Last modified October 21 15:41 EDT 2018. Contains 316424 sequences. (Running on oeis4.)