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A106301 Primes that do not divide any term of the Lucas 5-step 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 (list; graph; refs; listen; history; text; internal format)
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 (p-1)/d, where d is a small integer.

LINKS

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Fibonacci n-Step

MATHEMATICA

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

CROSSREFS

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).

Sequence in context: A140014 A188698 A209364 * A127623 A115474 A064976

Adjacent sequences:  A106298 A106299 A106300 * A106302 A106303 A106304

KEYWORD

nonn

AUTHOR

T. D. Noe, May 02 2005

STATUS

approved

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Last modified October 27 21:22 EDT 2020. Contains 338036 sequences. (Running on oeis4.)