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%I #11 Mar 24 2024 04:23:40
%S 2,691,3163,4259,5419,6637,6733,14923,25111,27947,29339,34123,34421,
%T 34757,42859,55207,57529,59693,61643,68897,70249,75991,82763,83177,
%U 85607,86441,87103,93169,93283,98573,106121,106433,114847,129589,132313
%N Primes that do not divide any term of the Lucas 5-step sequence A074048.
%C 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>.
%t 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 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 nonn
%O 1,1
%A _T. D. Noe_, May 02 2005