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approved
(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
Cf. A008344 (absolute differences).
Reinhard Zumkeller, <a href="/A086283/b086283.txt">Table of n, a(n) for n = 1..10000</a>
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editing
_John W. Layman (layman(AT)math.vt.edu), _, Aug 28 2003
First absol diffabsolute difference: 0,1,3,0,4,9,3,10,2,11,1,...
Second absol diffabsolute difference: 1,2,3,4,5,6,7,8,9,10,...
nonn,new
nonn
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
1,3
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.
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 absol diff: 0,1,3,0,4,9,3,10,2,11,1,...
Second absol diff: 1,2,3,4,5,6,7,8,9,10,...
Cf. A085059.
nonn
John W. Layman (layman(AT)math.vt.edu), Aug 28 2003
approved