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%I #13 Mar 24 2024 03:49:50
%S 2789,3847,4451,4751,5431,6203,8317,9533,9629,9907,10093,11839,13903,
%T 13907,14207,15823,16319,16759,19543,20939,21379,21859,25303,26683,
%U 29483,30871,31267,31699,32003,32771,33967,34963,36229,37061,39983
%N Primes that do not divide any term of the Lucas 4-step sequence A073817.
%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 A073817(k) mod p for increasing k and stopping when either A073817(k) mod p = 0 or the end of the period is reached. Interestingly, for all of these primes, the period of the sequence A073817(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=4; 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), A106301 (primes not dividing any Lucas 5-step number).
%K nonn
%O 1,1
%A _T. D. Noe_, May 02 2005