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 A106289 #12 Feb 16 2025 08:32:57 %S A106289 1,2,2,3,2,4,4,4,4,4,3,5,3,8,3,5,3,8,3,5,7,4,4,7,3,6,6,9,4,6,2,6,6,6, %T A106289 6,10,5,6,6,6,5,14,2,6,5,8,3,9,7,4,6,7,2,12,5,12,6,7,4,7,3,4,8,7,5,8, %U A106289 4,7,7,12,3,14,4,10,4,8,10,12,2,7,8,6,2,15,6,3,8,8,2,10,8,9,3,6,6,11,2,14,8 %N A106289 Number of different orbit lengths of the 4-step recursion mod n. %C A106289 Consider the 4-step recursion x(k)=x(k-1)+x(k-2)+x(k-3)+x(k-4) mod n. For any of the n^4 initial conditions x(1), x(2), x(3) and x(4) in Zn, the recursion has a finite period. Each of these n^4 vectors belongs to exactly one orbit. In general, there are only a few different orbit lengths for each n. For n=8, there are 4 different lengths: 1, 5, 10 and 20. The maximum possible length of an orbit is the period of the Fibonacci 4-step sequence mod n, which is essentially A106295(n). %H A106289 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>. %Y A106289 Cf. A106286 (orbits of 4-step sequences). %K A106289 nonn %O A106289 1,2 %A A106289 _T. D. Noe_, May 02 2005