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%I #10 Aug 04 2014 08:24:40
%S 0,1,1,0,1,0,2,2,2,2,0,2,0,2,0,1,1,2,2,1,1,0,1,0,2,0,1,0,3,3,3,3,3,3,
%T 3,3,0,3,0,3,0,3,0,3,0,1,1,3,3,1,1,3,3,1,1,0,1,0,3,0,1,0,3,0,1,0,2,2,
%U 2,2,3,3,3,3,2,2,2,2,0,2,0,2,0,3,0,3,0,2,0,2,0,1,1,2,2,1,1,3,3,1,1,2,2,1,1
%N Nim-values from game of Kopper's Nim.
%C Rows/columns 1-10 are A007814, A050603, A053399, A053384-A053890.
%C Comment from R. K. Guy: David Singmaster (zingmast(AT)sbu.ac.uk) sent me, about 5 years ago, a game he'd received from Bodo Koppers. It is played with two heaps of beans. The move is to remove one heap and split the other into two nonempty heaps. I'm not sure if Koppers invented it, or got it from elsewhere. I do not think that he analyzed it, but Singmaster did.
%H Reinhard Zumkeller, <a href="/A053398/b053398.txt">Rows n = 1..125 of triangle, flattened</a>
%F a(x, y) = place of last zero bit of (x-1) OR (y-1).
%F T(n,k) = A007814(A003986(n-1,k-1)+1). - _Reinhard Zumkeller_, Aug 04 2014
%o (Haskell)
%o a053398 :: Int -> Int -> Int
%o a053398 n k = a007814 $ a003986 (n - 1) (k - 1) + 1
%o a053398_row n = map (a053398 n) [1..n]
%o a053398_tabl = map a053398_row [1..]
%o -- _Reinhard Zumkeller_, Aug 04 2014
%Y Cf. A007814, A050603, A053399, A053384-A053890.
%Y Cf. A003986, A007814 (both edges & central terms & minima per row), A000523 (max per row), A245836 (row sums), A003987, A051775.
%K nonn,tabl,easy,nice
%O 1,7
%A _David W. Wilson_
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