A053890 -id:A053890 - cp's OEIS frontend

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

David W. Wilson

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.

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

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.

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

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

A053891 Squares composed of digits {1,3,4}.

Original entry on oeis.org

1, 4, 144, 441, 1444, 1411344, 431434441, 1441113444, 11414343334144, 134433311433444, 4334114143334143111441, 14431113411144114144433444, 331413131434411141441331411344, 444341333431434111311131411343131143441

Offset: 1

Patrick De Geest, Mar 15 2000

Zhao Hui Du, Table of n, a(n) for n = 1..15
Author?, Source(txt)
Patrick De Geest, Squares containing at most three distinct digits, Index entries for related sequences
H. Mishima, Sporadic tridigital solutions

Cf. A053890.

a(n) = A053890(n)^2.

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 04 2005
One more term from Jon E. Schoenfield, Sep 03 2006
Two more terms from Mishima's page added by Max Alekseyev, Jan 28 2012

cp's OEIS Frontend

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

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