A053398 Nim-values from game of Kopper's Nim.

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, 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, 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

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• tabl
• easy
• nice

Comments

Rows/columns 1-10 are A007814, A050603, A053399, A053384-A053890.

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.

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Crossrefs

Cf. A007814, A050603, A053399, A053384-A053890.

Cf. A003986, A007814 (both edges & central terms & minima per row), A000523 (max per row), A245836 (row sums), A003987, A051775.

Programs

Haskell

a053398 :: Int -> Int -> Int
a053398 n k = a007814 $ a003986 (n - 1) (k - 1) + 1
a053398_row n = map (a053398 n) [1..n]
a053398_tabl = map a053398_row [1..]
-- Reinhard Zumkeller, Aug 04 2014

Formula

a(x, y) = place of last zero bit of (x-1) OR (y-1).

T(n,k) = A007814(A003986(n-1,k-1)+1). - Reinhard Zumkeller, Aug 04 2014