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 A106299 #12 Feb 16 2025 08:32:57
%S A106299 2,103,199,211,421,757,883,907,991,1021,1123,1237,1543,1567,1621,1699,
%T A106299 1753,1873,2113,2539,2731,2797,2803,3391,3433,3463,3499,3613,3631,
%U A106299 3793,3853,3919,4093,4591,4723,4933,4951,4987,5107,5179,5527,5791,5839,6073
%N A106299 Primes that do not divide any term of the Lucas 3-step sequence A001644.
%C A106299 If a prime p divides a term a(k) of this sequence, then k must be less than the period of the sequence mod p. Hence these primes are found by computing A001644(k) mod p for increasing k and stopping when either A001644(k) mod p = 0 or the end of the period is reached. Interestingly, for all of these primes except 211, the period of the sequence A001644(k) mod p is (p-1)/d, where d is a small integer. The only other exceptional primes less than 1000000 are 23977 and 47093.
%H A106299 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>.
%t A106299 n=3; lst={}; Table[p=Prime[i]; a=Join[Table[ -1, {n-1}], {n}]; a=Mod[a, p]; a0=a; While[s=Mod[Plus@@a, p]; a=RotateLeft[a]; a[[n]]=s; !(a==a0 || s==0)]; If[s>0, AppendTo[lst, p]], {i, 1000}]; lst
%Y A106299 Cf. A053028 (primes not dividing any Lucas number), A106300 (primes not dividing any Lucas 4-step number), A106301 (primes not dividing any Lucas 5-step number).
%K A106299 nonn
%O A106299 1,1
%A A106299 _T. D. Noe_, May 02 2005