

A112374


Let T(n) = A000078(n+2), n >= 1; a(n) = smallest k such that n divides T(k).


0



1, 3, 6, 4, 6, 9, 8, 5, 9, 13, 20, 9, 10, 8, 6, 10, 53, 9, 48, 28, 18, 20, 35, 18, 76, 10, 9, 8, 7, 68, 20, 15, 20, 53, 30, 9, 58, 48, 78, 28, 19, 18, 63, 20, 68, 35, 28, 18, 46, 108, 76, 10, 158, 9, 52, 8, 87, 133, 18, 68, 51, 20, 46, 35, 78, 20, 17, 138, 35, 30, 230, 20, 72, 58, 76
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OFFSET

1,2


COMMENTS

Rank of apparition of n in the tetranacci numbers.  T. D. Noe, Dec 05 2005
This sequence is welldefined. 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 nstep 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 Kth term of the sequence. In general, K is much too large. However, it does show that every prime divides a term of every nstep Fibonacci sequence for n>1.  T. D. Noe, Dec 05 2005


LINKS

Table of n, a(n) for n=1..75.
J. L. Brenner, Linear Recurrence Relations, Amer. Math. Monthly, Vol. 61 (1954), 171173.
T. D. Noe and J. V. Post, Primes in Fibonacci nstep and Lucas nStep 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 nStep Number.


FORMULA

a(n) = Min{k: n  A000078(k)}.


MATHEMATICA

n=4; Table[a=Join[{1}, Table[0, {n1}]]; 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

Cf. A000078, A112269, A112305.
Sequence in context: A073233 A011287 A090963 * A222409 A093064 A197568
Adjacent sequences: A112371 A112372 A112373 * A112375 A112376 A112377


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Dec 02 2005


EXTENSIONS

Corrected by T. D. Noe, Dec 05 2005


STATUS

approved



