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 A106301 #12 Feb 16 2025 08:32:57
%S A106301 2,691,3163,4259,5419,6637,6733,14923,25111,27947,29339,34123,34421,
%T A106301 34757,42859,55207,57529,59693,61643,68897,70249,75991,82763,83177,
%U A106301 85607,86441,87103,93169,93283,98573,106121,106433,114847,129589,132313
%N A106301 Primes that do not divide any term of the Lucas 5-step sequence A074048.
%C A106301 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 A074048(k) mod p for increasing k and stopping when either A074048(k) mod p = 0 or the end of the period is reached. Interestingly, for all of these primes, the period of the sequence A074048(k) mod p appears to be (p-1)/d, where d is a small integer.
%H A106301 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>.
%t A106301 n=5; 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, 10000}]; lst
%Y A106301 Cf. A053028 (primes not dividing any Lucas number), A106299 (primes not dividing any Lucas 3-step number), A106300 (primes not dividing any Lucas 4-step number).
%K A106301 nonn
%O A106301 1,1
%A A106301 _T. D. Noe_, May 02 2005