A335162 - OEIS

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A335162

Array read by upward antidiagonals: T(n,k) (n >= 0, k >= 0) = nim k-th power of n.

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	`Rémy Sigrist, Table of n, a(n) for n = 0..20300` `J. H. Conway, Integral lexicographic codes, Discrete Mathematics 83.2-3 (1990): 219-235. See Table 3.` `Rémy Sigrist, PARI program for A335162` `Index entries for sequences related to Nim-multiplication`
	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	`Cf. A003987, A051775, A059971, A212200, A223541.` `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 A213888 A119337` `Adjacent sequences: A335159 A335160 A335161 * A335163 A335164 A335165`
	KEYWORD	`nonn,tabl`
	AUTHOR	`N. J. A. Sloane, Jun 08 2020`
	STATUS	`approved`

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Last modified May 28 18:07 EDT 2022. Contains 354120 sequences. (Running on oeis4.)