A046737 Reduced period of A000073 mod n.

1, 4, 13, 8, 31, 52, 16, 16, 13, 124, 110, 104, 56, 16, 403, 32, 96, 52, 120, 248, 208, 220, 553, 208, 155, 56, 39, 16, 140, 1612, 331, 64, 1430, 96, 496, 104, 469, 120, 728, 496, 560, 208, 308, 440, 403, 2212, 46, 416, 112, 620, 1248, 56, 52, 156

Offset

1,2

Comments

See A046738 for the period of the tribonacci numbers mod n. The ratio of the period to the reduced period is either 1 or 3. Robinson discusses the relationship between the period and the reduced period of a sequence. For the Fibonacci numbers, the analogous sequence is A001177. - T. D. Noe, Jan 14 2009

Links

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

D. W. Robinson, A note on linear recurrent sequences modulo m, Amer. Math. Monthly 73 (1966), 619-621.

Example

From T. D. Noe, Jan 14 2009: (Start)
The tribonacci sequence (starting with 1) mod 7 has a period that repeats
  1, 1, 2, 4, 0, 6, 3, 2, 4, 2, 1, 0, 3, 4, 0, 0,
  4, 4, 1, 2, 0, 3, 5, 1, 2, 1, 4, 0, 5, 2, 0, 0,
  2, 2, 4, 1, 0, 5, 6, 4, 1, 4, 2, 0, 6, 1, 0, 0.
The first pair of zeros occurs at the 16th term. Hence a(7)=16.
(End)

Crossrefs

Cf. A000073, A001177, A046738, A154753 (restriction to prime indices), A386236.

Sequence in context: A170844 A051432 A064461 * A046738 A095324 A264341

Adjacent sequences: A046734 A046735 A046736 * A046738 A046739 A046740

Keyword

nonn

Author

David W. Wilson

Extensions

Improved name from T. D. Noe, Jan 14 2009

Status

approved