A335162 -id:A335162 - cp's OEIS frontend

A335163 Nim n-th power of 4.

1, 4, 6, 14, 5, 2, 8, 11, 7, 10, 3, 12, 13, 9, 15, 1, 4, 6, 14, 5, 2, 8, 11, 7, 10, 3, 12, 13, 9, 15, 1, 4, 6, 14, 5, 2, 8, 11, 7, 10, 3, 12, 13, 9, 15, 1, 4, 6, 14, 5, 2, 8, 11, 7, 10, 3, 12, 13, 9, 15, 1, 4, 6, 14, 5, 2, 8, 11, 7, 10, 3, 12, 13, 9, 15, 1, 4

Offset: 0

N. J. A. Sloane, Jun 12 2020

nonn

J. H. Conway, Integral lexicographic codes, Discrete Mathematics 83.2-3 (1990): 219-235. See Table 3.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

A row of the array in A335162.

Vec((1 + 4*x + 6*x^2 + 14*x^3 + 5*x^4 + 2*x^5 + 8*x^6 + 11*x^7 + 7*x^8 + 10*x^9 + 3*x^10 + 12*x^11 + 13*x^12 + 9*x^13 + 15*x^14) / (1 - x^15) + O(x^80)) \\ Colin Barker, Jun 16 2020

a(n)=[1, 4, 6, 14, 5, 2, 8, 11, 7, 10, 3, 12, 13, 9, 15][n%15+1]; \\ Joerg Arndt, Jun 16 2020

a(n+15) = a(n). - Rémy Sigrist, Jun 12 2020

G.f.: (1 + 4*x + 6*x^2 + 14*x^3 + 5*x^4 + 2*x^5 + 8*x^6 + 11*x^7 + 7*x^8 + 10*x^9 + 3*x^10 + 12*x^11 + 13*x^12 + 9*x^13 + 15*x^14) / (1 - x^15). - Colin Barker, Jun 16 2020

More terms from Rémy Sigrist, Jun 12 2020

A335169 Nim n-th power of 10.

Original entry on oeis.org

1, 10, 14, 13, 8, 1, 10, 14, 13, 8, 1, 10, 14, 13, 8, 1, 10, 14, 13, 8, 1, 10, 14, 13, 8, 1, 10, 14, 13, 8, 1, 10, 14, 13, 8, 1, 10, 14, 13, 8, 1, 10, 14, 13, 8, 1, 10, 14, 13, 8, 1, 10, 14, 13, 8, 1, 10, 14, 13, 8, 1, 10, 14, 13, 8, 1, 10, 14, 13, 8, 1, 10

Offset: 0

N. J. A. Sloane, Jun 12 2020

nonn

J. H. Conway, Integral lexicographic codes, Discrete Mathematics 83.2-3 (1990): 219-235. See Table 3.

A row of the array in A335162.

a(n+5) = a(n). - Rémy Sigrist, Jun 12 2020

More terms from Rémy Sigrist, Jun 12 2020

A356522 Numbers that are nim cubes; numbers in A335170.

Original entry on oeis.org

0, 1, 8, 10, 13, 14, 16, 17, 20, 21, 24, 25, 30, 31, 36, 38, 45, 47, 49, 50, 61, 62, 72, 74, 76, 78, 88, 90, 93, 95, 105, 106, 108, 111, 113, 114, 117, 118, 128, 130, 131, 133, 136, 138, 139, 141, 145, 151, 152, 158, 160, 161, 163, 167, 169, 170, 171, 173, 177, 182, 186

Offset: 1

Jianing Song, Aug 10 2022

nonn

Also numbers in A335172, or numbers that are nim (3*2^m)-th powers for each m.

There are (2^2^k - 1)/3 + 1 terms <= 2^2^k - 1 for each k >= 1. This is because {0,1,...,2^2^k-1} together with the nim operations makes a field isomorphic to GF(2^2^k).

			8 is a term because (6 N* 6) N* 6 = 5 N* 6 = 8, where N* denotes the nim multiplication.

Jianing Song, Table of n, a(n) for n = 1..21846 (all terms <= 2^2^4 - 1 = 65535)

Cf. A051175, A335170, A335172. See also A335162 for nim powers.

lim(N) = Set(vector(2^2^N, i, A335170(i-1))) \\ A335170 is the function a from Rémy Sigrist in A335170; lim(N) gives all terms <= 2^2^N - 1

A335164 Nim n-th power of 5.

Original entry on oeis.org

1, 5, 7, 13, 4, 2, 10, 9, 6, 8, 3, 15, 14, 11, 12, 1, 5, 7, 13, 4, 2, 10, 9, 6, 8, 3, 15, 14, 11, 12, 1, 5, 7, 13, 4, 2, 10, 9, 6, 8, 3, 15, 14, 11, 12, 1, 5, 7, 13, 4, 2, 10, 9, 6, 8, 3, 15, 14, 11, 12, 1, 5, 7, 13, 4, 2, 10, 9, 6, 8, 3, 15, 14, 11, 12, 1, 5

Offset: 0

N. J. A. Sloane, Jun 12 2020

nonn

J. H. Conway, Integral lexicographic codes, Discrete Mathematics 83.2-3 (1990): 219-235. See Table 3.

A row of the array in A335162.

a(n+15) = a(n). - Rémy Sigrist, Jun 12 2020

More terms from Rémy Sigrist, Jun 12 2020

A335165 Nim n-th power of 6.

Original entry on oeis.org

1, 6, 5, 8, 7, 3, 13, 15, 4, 14, 2, 11, 10, 12, 9, 1, 6, 5, 8, 7, 3, 13, 15, 4, 14, 2, 11, 10, 12, 9, 1, 6, 5, 8, 7, 3, 13, 15, 4, 14, 2, 11, 10, 12, 9, 1, 6, 5, 8, 7, 3, 13, 15, 4, 14, 2, 11, 10, 12, 9, 1, 6, 5, 8, 7, 3, 13, 15, 4, 14, 2, 11, 10, 12, 9, 1, 6

Offset: 0

N. J. A. Sloane, Jun 12 2020

nonn

J. H. Conway, Integral lexicographic codes, Discrete Mathematics 83.2-3 (1990): 219-235. See Table 3.

A row of the array in A335162.

a(n+15) = a(n). - Rémy Sigrist, Jun 12 2020

More terms from Rémy Sigrist, Jun 12 2020

A335166 Nim n-th power of 7.

Original entry on oeis.org

1, 7, 4, 10, 6, 3, 14, 12, 5, 13, 2, 9, 8, 15, 11, 1, 7, 4, 10, 6, 3, 14, 12, 5, 13, 2, 9, 8, 15, 11, 1, 7, 4, 10, 6, 3, 14, 12, 5, 13, 2, 9, 8, 15, 11, 1, 7, 4, 10, 6, 3, 14, 12, 5, 13, 2, 9, 8, 15, 11, 1, 7, 4, 10, 6, 3, 14, 12, 5, 13, 2, 9, 8, 15, 11, 1, 7

Offset: 0

N. J. A. Sloane, Jun 12 2020

nonn

J. H. Conway, Integral lexicographic codes, Discrete Mathematics 83.2-3 (1990): 219-235. See Table 3.

A row of the array in A335162.

PadRight[{},120,{1,7,4,10,6,3,14,12,5,13,2,9,8,15,11}] (* Harvey P. Dale, Jan 02 2022 *)

a(n+15) = a(n). - Rémy Sigrist, Jun 12 2020

More terms from Rémy Sigrist, Jun 12 2020

A335167 Nim n-th power of 8.

Original entry on oeis.org

1, 8, 13, 14, 10, 1, 8, 13, 14, 10, 1, 8, 13, 14, 10, 1, 8, 13, 14, 10, 1, 8, 13, 14, 10, 1, 8, 13, 14, 10, 1, 8, 13, 14, 10, 1, 8, 13, 14, 10, 1, 8, 13, 14, 10, 1, 8, 13, 14, 10, 1, 8, 13, 14, 10, 1, 8, 13, 14, 10, 1, 8, 13, 14, 10, 1, 8, 13, 14, 10, 1, 8, 13

Offset: 0

N. J. A. Sloane, Jun 12 2020

nonn

J. H. Conway, Integral lexicographic codes, Discrete Mathematics 83.2-3 (1990): 219-235. See Table 3.

A row of the array in A335162.

a(n+5) = a(n). - Rémy Sigrist, Jun 12 2020

More terms from Rémy Sigrist, Jun 12 2020

A335168 Nim n-th power of 9.

Original entry on oeis.org

1, 9, 12, 10, 11, 2, 14, 4, 15, 13, 3, 7, 8, 5, 6, 1, 9, 12, 10, 11, 2, 14, 4, 15, 13, 3, 7, 8, 5, 6, 1, 9, 12, 10, 11, 2, 14, 4, 15, 13, 3, 7, 8, 5, 6, 1, 9, 12, 10, 11, 2, 14, 4, 15, 13, 3, 7, 8, 5, 6, 1, 9, 12, 10, 11, 2, 14, 4, 15, 13, 3, 7, 8, 5, 6, 1, 9

Offset: 0

N. J. A. Sloane, Jun 12 2020

nonn

J. H. Conway, Integral lexicographic codes, Discrete Mathematics 83.2-3 (1990): 219-235. See Table 3.

A row of the array in A335162.

a(n+15) = a(n). - Rémy Sigrist, Jun 12 2020

More terms from Rémy Sigrist, Jun 12 2020

cp's OEIS Frontend

A335163 Nim n-th power of 4.

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A335169 Nim n-th power of 10.

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A356522 Numbers that are nim cubes; numbers in A335170.

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A335164 Nim n-th power of 5.

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A335165 Nim n-th power of 6.

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A335166 Nim n-th power of 7.

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A335167 Nim n-th power of 8.

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A335168 Nim n-th power of 9.

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