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 A106288 #12 Feb 16 2025 08:32:57 %S A106288 1,3,2,4,2,6,3,5,3,6,4,8,3,6,4,6,3,9,3,8,6,8,2,10,3,5,4,8,3,12,2,7,8, %T A106288 5,6,12,2,6,6,10,3,12,3,11,6,6,3,12,5,9,6,7,3,12,8,9,6,6,2,16,3,6,7,8, %U A106288 6,16,2,6,4,12,2,15,3,6,6,8,10,10,3,12,5,5,3,16,6,7,6,14,2,18,6,8,4,6,6 %N A106288 Number of different orbit lengths of the 3-step recursion mod n. %C A106288 Consider the 3-step recursion x(k)=x(k-1)+x(k-2)+x(k-3) mod n. For any of the n^3 initial conditions x(1), x(2) and x(3) in Zn, the recursion has a finite period. Each of these n^3 vectors belongs to exactly one orbit. In general, there are only a few different orbit lengths for each n. For n=8, there are 5 different lengths: 1, 2, 4, 8 and 16. The maximum possible length of an orbit is A046738(n), the period of the Fibonacci 3-step sequence mod n. %H A106288 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>. %Y A106288 Cf. A106285 (orbits of 3-step sequences), A106307 (primes that yield a simple orbit structure in 3-step recursions). %K A106288 nonn %O A106288 1,2 %A A106288 _T. D. Noe_, May 02 2005