This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A282779 #18 Dec 20 2023 12:13:45
%S A282779 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,
%T A282779 9,28,29,30,31,32,33,34,35,12,37,38,39,40,41,42,43,44,15,46,47,48,49,
%U A282779 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
%N A282779 Period of cubes mod n.
%C A282779 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_).
%C A282779 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.
%C A282779 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.
%H A282779 Ray Chandler, <a href="/A282779/b282779.txt">Table of n, a(n) for n = 1..10000</a>
%H A282779 Ilya Gutkovskiy, <a href="/A282779/a282779.pdf">Extended graphical example</a>
%H A282779 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1).
%F A282779 Apparently: a(n) = 2*a(n-9) - a(n-18).
%F A282779 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
%e A282779 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.
%t A282779 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}]
%Y A282779 Cf. A000035, A000578, A008960, A010872, A010875, A046530, A070471, A070472, A109718, A109753, A167176, A186646.
%K A282779 nonn,easy
%O A282779 1,2
%A A282779 _Ilya Gutkovskiy_, Feb 21 2017