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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,...}.

%I A086283 #6 Oct 20 2014 16:14:15
%S A086283 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 A086283 5,11,45,40,5,1,37,34,71,69,31,30,69,69,29,110,71,153,27,108,73,155,
%U A086283 25,106,75,157,23,104,77,159,21,102,79,161,19,100,81,163,17,98,83,1,15,98
%N 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,...}.
%C A086283 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 A086283 Reinhard Zumkeller, <a href="/A086283/b086283.txt">Table of n, a(n) for n = 1..10000</a>
%e A086283 For the initial terms, no smaller positive terms work than
%e A086283 Sequence {a(n)}: 1,1,2,5,5,1,10,7,17,15,4,3,...
%e A086283 First absolute difference: 0,1,3,0,4,9,3,10,2,11,1,...
%e A086283 Second absolute difference: 1,2,3,4,5,6,7,8,9,10,...
%o A086283 (Haskell)
%o A086283 a086283 n = x086283_list !! (n-1)
%o A086283 a086283_list = 1 : 1 : f 1 0 [1..] where
%o A086283    f x y (z:zs) = u : f u (abs $ x - u) zs where
%o A086283      u = minimum [if v < x then x - v else x + v |
%o A086283                   v <- if y < z then [y + z] else [y + z, y - z]]
%o A086283 -- _Reinhard Zumkeller_, Oct 17 2014
%Y A086283 Cf. A085059.
%Y A086283  Cf. A008344 (absolute differences).
%K A086283 nonn
%O A086283 1,3
%A A086283 _John W. Layman_, Aug 28 2003