OFFSET
1,2
COMMENTS
Rank of apparition of n in the tetranacci numbers. - T. D. Noe, Dec 05 2005
This sequence is well-defined. Proof by T. D. Noe: for every prime p, Brenner proves we can find k(p) such that p divides the k(p)-th term of n-step Fibonacci. Using Brenner's methods, we know that p will also divide every j*k(p)-th term of the sequence for any j>0. We use this last fact to go to the general case: For integer m, we can find a term that m divides as follows: (1) factor m into primes: m = p1^e1 p2^e2...pr^er, (2) let K = m k(p1) k(p2)...k(pr) / (p1 p2 ... pr) (3) then m will divide the K-th term of the sequence. In general, K is much too large. However, it does show that every prime divides a term of every n-step Fibonacci sequence for n>1. - T. D. Noe, Dec 05 2005
LINKS
J. L. Brenner, Linear Recurrence Relations, Amer. Math. Monthly, Vol. 61 (1954), 171-173.
T. D. Noe and J. V. Post, Primes in Fibonacci n-step and Lucas n-Step Sequences, J. Integer Seq. 8, Article 05.4.4, 2005.
Eric Weisstein's World of Mathematics, Tetranacci Number.
Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.
FORMULA
a(n) = Min{k: n | A000078(k)}.
MATHEMATICA
n=4; Table[a=Join[{1}, Table[0, {n-1}]]; k=0; While[k++; s=Mod[Plus@@a, i]; a=RotateLeft[a]; a[[n]]=s; s!=0]; k, {i, 100}] (* T. D. Noe, Dec 05 2005 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Dec 02 2005
EXTENSIONS
Corrected by T. D. Noe, Dec 05 2005
STATUS
approved