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Search: id:A112374
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| A112374 |
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Let T(n) = A000078(n+2), n >= 1; a(n) = smallest k such that n divides T(k). |
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1
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Rank of apparition of n in the tetranacci numbers. - T. D. Noe (noe(AT)sspectra.com), Dec 05 2005
This sequence is well-defined. Proof by T. D. Noe (noe(AT)sspectra.com): 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 (noe(AT)sspectra.com), Dec 05 2005
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REFERENCES
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J. L. Brenner, Linear Recurrence Relations, Amer. Math. Monthly, Vol. 61 (1954), 171-173.
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LINKS
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Noe, T. D. and Post, J. V. "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.
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FORMULA
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a(n) = Min{k: n | A000078(k)}.
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MATHEMATICA
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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}] (Noe)
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CROSSREFS
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Cf. A000078, A112269, A112305.
Sequence in context: A073233 A011287 A090963 this_sequence A093064 A136612 A004546
Adjacent sequences: A112371 A112372 A112373 this_sequence A112375 A112376 A112377
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Dec 02 2005
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Dec 05 2005
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