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

Author

N. J. A. Sloane, Nov 30 2005

Keywords

• nonn

Comments

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

Examples

			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.
		

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.

Crossrefs

Cf. A000073.

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

Programs

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 *)