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 A106293 #23 Aug 27 2025 00:08:57
%S A106293 1,1,13,4,31,13,48,8,39,31,10,52,168,48,403,16,96,39,360,124,624,10,
%T A106293 553,104,155,168,117,48,140,403,331,32,130,96,1488,156,469,360,2184,
%U A106293 248,560,624,308,20,1209,553,46,208,336,155,1248,168,52,117,310,48,4680,140
%N A106293 Period of the Lucas 3-step sequence A001644 mod n.
%C A106293 This sequence can differ from the corresponding Fibonacci sequence (A046738) only when n is a multiple of 2 or 11 because the discriminant of the characteristic polynomial x^3-x^2-x-1 is -44. [Clarified by _Avery Diep_, Aug 22 2025]
%C A106293 a(n) divides A046738(n). - _Avery Diep_, Aug 22 2025
%H A106293 T. D. Noe, <a href="/A106293/b106293.txt">Table of n, a(n) for n=1..1000</a>
%H A106293 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>.
%F A106293 Let the prime factorization of n be p1^e1...pk^ek. Then a(n) = lcm(a(p1^e1), ..., a(pk^ek)).
%t A106293 n=3; Table[p=i; a=Join[Table[ -1, {n-1}], {n}]; a=Mod[a, p]; a0=a; k=0; While[k++; s=Mod[Plus@@a, p]; a=RotateLeft[a]; a[[n]]=s; a!=a0]; k, {i, 60}]
%Y A106293 Cf. A046738 (period of Fibonacci 3-step sequence mod n), A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1).
%K A106293 nonn,changed
%O A106293 1,3
%A A106293 _T. D. Noe_, May 02 2005