A112305 Let T(n) = A000073(n+1), n >= 1; a(n) = smallest k such that n divides T(k).

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

Offset

1,2

Comments

Brenner proves that every prime divides some tribonacci number T(n). The Mathematica program computes similar sequences for any n-step Fibonacci sequence.

References

Ed Pegg, Jr., Posting to Sequence Fan mailing list, Nov 30, 2005

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

J. L. Brenner, Linear Recurrence Relations, Amer. Math. Monthly, Vol. 61 (1954), 171-173.

Eric Weisstein's World of Mathematics, Tribonacci Number.

Example

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.

Mathematica

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}] (* T. D. Noe *)

Crossrefs

Cf. A000073.

Cf. A112312 (least k such that prime(n) divides T(k)).

Sequence in context: A216627 A355927 A365724 * A231396 A231463 A218616

Adjacent sequences: A112302 A112303 A112304 * A112306 A112307 A112308

Keyword

nonn

Author

N. J. A. Sloane, Nov 30 2005

Status

approved