A154753 Reduced period of the Fibonacci 3-step sequence A000073 mod prime(n).

4, 13, 31, 16, 110, 56, 96, 120, 553, 140, 331, 469, 560, 308, 46, 52, 3541, 620, 1519, 5113, 1776, 1040, 287, 8011, 3169, 680, 17, 1272, 330, 12883, 1792, 5720, 18907, 1288, 7400, 950, 8269, 54, 9296, 2494, 32221, 10981, 36673, 1552, 3234, 66, 1855

Offset

1,1

Comments

The Fibonacci 3-step (tribonacci) sequence t(k) begins (with offset -2) 1,0,0. For a prime p, the reduced period r is the least number such that p divides both t(r-1) and t(r); i.e., "0,0" appears in the sequence mod p. The ratio of the period A106302 and the reduced period is either 1 or 3; see A154754.

Links

Table of n, a(n) for n=1..47.

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

Formula

a(n) = A046738(prime(n)).

Example

The tribonacci sequence (starting with 1) mod 7 begins with the 48 terms 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 "0,0" terms occur at index 16. Hence a(4)=16.

Crossrefs

Cf. A046737, A046738.

Sequence in context: A218213 A075880 A042487 * A335981 A191189 A106302

Adjacent sequences: A154750 A154751 A154752 * A154754 A154755 A154756

Keyword

nonn

Author

T. D. Noe, Jan 15 2009

Status

approved