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Search: id:A112305
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| A112305 |
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Let T(n) = A00073(n+1), n >= 1; a(n) = smallest k such that n divides T(k). |
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4
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| 1, 3, 7, 4, 14, 7, 5, 7, 9, 19, 8, 7, 6, 12, 52, 15, 28, 12, 18, 31, 12, 8, 29, 7, 30, 39, 9, 12, 77, 52, 14, 15, 35, 28, 21, 12, 19, 28, 39, 31, 35, 12, 82, 8, 52, 55, 29, 64, 15, 52, 124, 39, 33, 35, 14, 12, 103, 123, 64, 52, 68, 60, 12, 15, 52, 35, 100, 28, 117
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Brenner proves that every prime divides some tribonacci number T(n). The Mathematica program computes similar sequences for any n-step Fibonacci sequence.
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REFERENCES
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J. L. Brenner, Linear Recurrence Relations, Amer. Math. Monthly, Vol. 61 (1954), 171-173.
Ed Pegg, Jr., Posting to Sequence Fan mailing list, Nov 30, 2005
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LINKS
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Eric Weisstein's World of Mathematics, MathWorld: Tribonacci Number
Eric Weisstein's World of Mathematics, Tribonacci Number
Eric Weisstein's World of Mathematics, Tribonacci Number
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EXAMPLE
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T(1), T(2), T(3), T(4), ... are 1,1,2,4,7,13,24,...; a(3) = 7 because 3 first divides T(7) = A000073(8) = 24.
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MATHEMATICA
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n=3; 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. A000073.
Cf. A112312 (least k such that prime(n) divides T(k)).
Adjacent sequences: A112302 A112303 A112304 this_sequence A112306 A112307 A112308
Sequence in context: A019831 A016619 A066538 this_sequence A114691 A023639 A086242
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KEYWORD
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nonn
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AUTHOR
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njas, Nov 30 2005
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