

A106301


Primes that do not divide any term of the Lucas 5step sequence A074048.


2



2, 691, 3163, 4259, 5419, 6637, 6733, 14923, 25111, 27947, 29339, 34123, 34421, 34757, 42859, 55207, 57529, 59693, 61643, 68897, 70249, 75991, 82763, 83177, 85607, 86441, 87103, 93169, 93283, 98573, 106121, 106433, 114847, 129589, 132313
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OFFSET

1,1


COMMENTS

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 (p1)/d, where d is a small integer.


LINKS



MATHEMATICA

n=5; lst={}; Table[p=Prime[i]; a=Join[Table[ 1, {n1}], {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


CROSSREFS

Cf. A053028 (primes not dividing any Lucas number), A106299 (primes not dividing any Lucas 3step number), A106300 (primes not dividing any Lucas 4step number).


KEYWORD

nonn


AUTHOR



STATUS

approved



