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%I #22 Feb 28 2023 05:34:34
%S 1,3,7,4,14,7,5,7,9,19,8,7,6,12,52,15,28,12,18,31,12,8,29,7,30,39,9,
%T 12,77,52,14,15,35,28,21,12,19,28,39,31,35,12,82,8,52,55,29,64,15,52,
%U 124,39,33,35,14,12,103,123,64,52,68,60,12,15,52,35,100,28,117
%N Let T(n) = A000073(n+1), n >= 1; a(n) = smallest k such that n divides T(k).
%C Brenner proves that every prime divides some tribonacci number T(n). The Mathematica program computes similar sequences for any n-step Fibonacci sequence.
%D Ed Pegg, Jr., Posting to Sequence Fan mailing list, Nov 30, 2005
%H T. D. Noe, <a href="/A112305/b112305.txt">Table of n, a(n) for n = 1..1000</a>
%H J. L. Brenner, <a href="http://www.jstor.org/stable/2307216">Linear Recurrence Relations</a>, Amer. Math. Monthly, Vol. 61 (1954), 171-173.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TribonacciNumber.html">Tribonacci Number</a>.
%e T(1), T(2), T(3), T(4), ... are 1,1,2,4,7,13,24,...; a(3) = 7 because 3 first divides T(7) = A000073(8) = 24.
%t n=3; Table[a=Join[{1}, Table[0, {n-1}]]; k=0; While[k++; s=Mod[Plus@@a, i]; a=RotateLeft[a]; a[[n]]=s; s!=0]; k, {i, 100}] (* _T. D. Noe_ *)
%Y Cf. A000073.
%Y Cf. A112312 (least k such that prime(n) divides T(k)).
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Nov 30 2005
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