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 A154753 Reduced period of the Fibonacci 3-step sequence A000073 mod prime(n). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 4 15:45 EDT 2024. Contains 374923 sequences. (Running on oeis4.)