A106300 Primes that do not divide any term of the Lucas 4-step sequence A073817.

2789, 3847, 4451, 4751, 5431, 6203, 8317, 9533, 9629, 9907, 10093, 11839, 13903, 13907, 14207, 15823, 16319, 16759, 19543, 20939, 21379, 21859, 25303, 26683, 29483, 30871, 31267, 31699, 32003, 32771, 33967, 34963, 36229, 37061, 39983

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 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.

Links

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

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

Mathematica

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

Crossrefs

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).

Sequence in context: A206516 A119377 A014895 * A252601 A233923 A340174

Adjacent sequences: A106297 A106298 A106299 * A106301 A106302 A106303

Keyword

nonn

Author

T. D. Noe, May 02 2005

Status

approved