The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #9 Oct 01 2017 09:36:31
%S 4,13,31,16,110,56,96,120,553,140,331,469,560,308,46,52,3541,620,1519,
%T 5113,1776,1040,287,8011,3169,680,17,1272,330,12883,1792,5720,18907,
%U 1288,7400,950,8269,54,9296,2494,32221,10981,36673,1552,3234,66,1855
%N Reduced period of the Fibonacci 3-step sequence A000073 mod prime(n).
%C 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.
%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.
%F a(n) = A046738(prime(n)).
%e 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.
%Y Cf. A046737, A046738.
%K nonn
%O 1,1
%A _T. D. Noe_, Jan 15 2009