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Reduced period of A000073 mod n.
4

%I #17 May 25 2024 21:31:42

%S 1,4,13,8,31,52,16,16,13,124,110,104,56,16,403,32,96,52,120,248,208,

%T 220,553,208,155,56,39,16,140,1612,331,64,1430,96,496,104,469,120,728,

%U 496,560,208,308,440,403,2212,46,416,112,620,1248,56,52,156

%N Reduced period of A000073 mod n.

%C 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

%H T. D. Noe, <a href="/A046737/b046737.txt">Table of n, a(n) for n=1..1000</a>

%H D. W. Robinson, <a href="http://www.jstor.org/stable/2314796">A note on linear recurrent sequences modulo m</a>, Amer. Math. Monthly 73 (1966), 619-621.

%e 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. - _T. D. Noe_, Jan 14 2009

%Y Cf. A000073, A001177, A046738.

%K nonn

%O 1,2

%A _David W. Wilson_

%E Improved name from _T. D. Noe_, Jan 14 2009