A070471 -id:A070471 - cp's OEIS frontend

A070690 Duplicate of A070471.

0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0

Offset: 0

dead

A282779 Period of cubes mod n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 3, 10, 11, 12, 13, 14, 15, 16, 17, 6, 19, 20, 21, 22, 23, 24, 25, 26, 9, 28, 29, 30, 31, 32, 33, 34, 35, 12, 37, 38, 39, 40, 41, 42, 43, 44, 15, 46, 47, 48, 49, 50, 51, 52, 53, 18, 55, 56, 57, 58, 59, 60, 61, 62, 21, 64, 65, 66, 67, 68, 69, 70, 71, 24, 73, 74, 75, 76, 77, 78, 79, 80, 27

Offset: 1

Ilya Gutkovskiy, Feb 21 2017

The length of the period of A000035 (n=2), A010872 (n=3), A109718 (n=4), A070471 (n=5), A010875 (n=6), A070472 (n=7), A109753 (n=8), A167176 (n=9), A008960 (n = 10), etc. (see also comment in A000578 from R. J. Mathar).
Conjecture: let a_p(n) be the length of the period of the sequence k^p mod n where p is a prime, then a_p(n) = n/p if n == 0 (mod p^2) else a_p(n) = n.
For example: sequence k^7 mod 98 gives 1, 30, 31, 18, 19, 48, 49, 50, 79, 80, 67, 68, 97, 0, 1, 30, 31, 18, 19, 48, 49, 50, 79, 80, 67, 68, 97, 0, ... (period 14), 7 is a prime, 98 == 0 (mod 7^2) and 98/7 = 14.

			a(9) = 3 because reading 1, 8, 27, 64, 125, 216, 343, 512, ... modulo 9 gives 1, 8, 0, 1, 8, 0, 1, 8, 0, ... with period length 3.

Ray Chandler, Table of n, a(n) for n = 1..10000
Ilya Gutkovskiy, Extended graphical example
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Cf. A000035, A000578, A008960, A010872, A010875, A046530, A070471, A070472, A109718, A109753, A167176, A186646.

a[1] = 1; a[n_] := For[k = 1, True, k++, If[Mod[k^3, n] == 0 && Mod[(k + 1)^3 , n] == 1, Return[k]]]; Table[a[n], {n, 1, 81}]

Apparently: a(n) = 2*a(n-9) - a(n-18).

Empirical g.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 8*x^7 + 3*x^8 + 8*x^9 + 7*x^10 + 6*x^11 + 5*x^12 + 4*x^13 + 3*x^14 + 2*x^15 + x^16) / ((1 - x)^2*(1 + x + x^2)^2*(1 + x^3 + x^6)^2). - Colin Barker, Feb 21 2017

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A070690 Duplicate of A070471.

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A282779 Period of cubes mod n.

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