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A335162 Array read by upward antidiagonals: T(n,k) (n >= 0, k >= 0) = nim k-th power of n. 19
1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 3, 1, 0, 1, 4, 2, 1, 1, 0, 1, 5, 6, 1, 2, 1, 0, 1, 6, 7, 14, 3, 3, 1, 0, 1, 7, 5, 13, 5, 2, 1, 1, 0, 1, 8, 4, 8, 4, 2, 1, 2, 1, 0, 1, 9, 13, 10, 7, 2, 8, 3, 3, 1, 0, 1, 10, 12, 14, 6, 3, 10, 11, 2, 1, 1, 0, 1, 11, 14, 10, 10, 3, 13, 9, 7, 1, 2, 1, 0, 1, 12, 15, 13, 11, 1, 14, 15, 6, 10, 3, 3, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,8
COMMENTS
Although the nim-addition table (A003987) and nim-multiplication table (A051775) can be found in Conway's "On Numbers and Games", and in the Berlekamp-Conway-Guy "Winning Ways", this exponentiation-table seems to have been omitted.
The n-th row is A212200(n)-periodic. - Rémy Sigrist, Jun 12 2020
LINKS
J. H. Conway, Integral lexicographic codes, Discrete Mathematics 83.2-3 (1990): 219-235. See Table 3.
FORMULA
From Rémy Sigrist, Jun 12 2020: (Start)
T(n, A212200(n)) = 1 for any n > 0.
T(n, n) = A059971(n).
(End)
EXAMPLE
The array begins:
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...,
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, ...,
1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, ...,
1, 4, 6,14, 5, 2, 8,11, 7,10, 3,12,13, 9,15, 1, 4, 6, ...,
1, 5, 7,13, 4, 2,10, 9, 6, 8, 3,15,14,11,12, 1, 5, 7, ...,
1, 6, 5, 8, 7, 3,13,15, 4,14, 2,11,10,12, 9, 1, 6, 5, ...,
1, 7, 4,10, 6, 3,14,12, 5,13, 2, 9, 8,15,11, 1, 7, 4, ...,
1, 8,13,14,10, 1, 8,13,14,10, 1, 8,13,14,10, 1, 8,13, ...,
1, 9,12,10,11, 2,14, 4,15,13, 3, 7, 8, 5, 6, 1, 9,12, ...,
1,10,14,13, 8, 1,10,14,13, 8, 1,10,14,13, 8, 1, 10,14, ...,
1,11,15, 8, 9, 2,13, 5,12,14, 3, 6,10, 4, 7, 1, 11,15, ...,
1,12,11,14,15, 3, 8, 6, 9,10, 2, 4,13, 7, 5, 1, 12,11, ...,
1,13,10, 8,14, 1,13,10, 8,14, 1,13,10, 8,14, 1, 13,10, ...,
1,14, 8,10,13, 1,14, 8,10,13, 1,14, 8,10,13, 1, 14, 8, ...,
1,15, 9,13,12, 3,10, 7,11, 8, 2, 5,14, 6, 4, 1, 15, 9, ...
...
The initial antidiagonals are:
[1]
[1, 0]
[1, 1, 0]
[1, 2, 1, 0]
[1, 3, 3, 1, 0]
[1, 4, 2, 1, 1, 0]
[1, 5, 6, 1, 2, 1, 0]
[1, 6, 7, 14, 3, 3, 1, 0]
[1, 7, 5, 13, 5, 2, 1, 1, 0]
[1, 8, 4, 8, 4, 2, 1, 2, 1, 0]
[1, 9, 13, 10, 7, 2, 8, 3, 3, 1, 0]
[1, 10, 12, 14, 6, 3, 10, 11, 2, 1, 1, 0]
[1, 11, 14, 10, 10, 3, 13, 9, 7, 1, 2, 1, 0]
[1, 12, 15, 13, 11, 1, 14, 15, 6, 10, 3, 3, 1, 0]
...
PROG
(PARI) See Links section.
CROSSREFS
Rows: for nim-powers of 4 through 10 see A335163-A335169.
Columns: for nim-squares, cubes, fourth, fifth, sixth, seventh and eighth powers see A006042, A335170, A335535, A335171, A335172, A335173 and A335536.
Sequence in context: A213887 A279589 A279594 * A077593 A363778 A213888
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jun 08 2020
STATUS
approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)