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

1,7

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

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

Prog

(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

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.

Sequence in context: A306216 A238451 A205777 * A065833 A245476 A215884

Adjacent sequences: A053395 A053396 A053397 * A053399 A053400 A053401

Keyword

nonn,tabl,easy,nice

Author

David W. Wilson

Status

approved