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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 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 A363778 A213888 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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