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A106299 Primes that do not divide any term of the Lucas 3-step sequence A001644. 5
2, 103, 199, 211, 421, 757, 883, 907, 991, 1021, 1123, 1237, 1543, 1567, 1621, 1699, 1753, 1873, 2113, 2539, 2731, 2797, 2803, 3391, 3433, 3463, 3499, 3613, 3631, 3793, 3853, 3919, 4093, 4591, 4723, 4933, 4951, 4987, 5107, 5179, 5527, 5791, 5839, 6073 (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 A001644(k) mod p for increasing k and stopping when either A001644(k) mod p = 0 or the end of the period is reached. Interestingly, for all of these primes except 211, the period of the sequence A001644(k) mod p is (p-1)/d, where d is a small integer. The only other exceptional primes less than 1000000 are 23977 and 47093.

LINKS

Table of n, a(n) for n=1..44.

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

MATHEMATICA

n=3; 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, 1000}]; lst

CROSSREFS

Cf. A053028 (primes not dividing any Lucas number), A106300 (primes not dividing any Lucas 4-step number), A106301 (primes not dividing any Lucas 5-step number).

Sequence in context: A283624 A055693 A215964 * A176933 A246775 A281053

Adjacent sequences:  A106296 A106297 A106298 * A106300 A106301 A106302

KEYWORD

nonn

AUTHOR

T. D. Noe, May 02 2005

STATUS

approved

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Last modified August 9 12:05 EDT 2022. Contains 356026 sequences. (Running on oeis4.)