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%I #17 Oct 16 2013 18:01:22
%S 10,30,70,130,370,430,670,730,970,1030,1270,1570,1630,1930,2230,2770,
%T 2830,3130,3370,3670,3730,3970,4330,4570,4630,4870,5230,5470,5770,
%U 6070,6130,6430,6730,7270,7330,7570,7870,8230,8530,8770,8830,9070,9370,9970
%N Numbers n such that the period of Fibonacci numbers mod n is 3*(n+10).
%C Related to Pisano periods. Other than the initial term 10, these are a subset of the terms of A071774 multiplied by 10, where A071774 are numbers m such that Fibonacci numbers mod m = 2*(m+1). All A071774 terms multiplied by 10 have Pisano periods 3*(n+10) or (n+10). This sequence is the 3*(n+10) subset. A229467 is the n+10 subset.
%H Matthew Goers, <a href="/A229466/b229466.txt">Table of n, a(n) for n = 1..74</a>
%e The Pisano period of the Fibonacci numbers mod 30 = 120, which is 3*(30+10).
%e The Pisano period of the Fibonacci numbers mod 1570 = 4740, which is 3*(1570+10).
%t t = {}; Do[a = {1, 0}; a0 = a; k = 0; While[k++; s = Mod[Plus @@ a, n]; a = RotateLeft[a]; a[[2]] = s; k <= 3*(n + 10) && a != a0]; If[k == 3*(n + 10), AppendTo[t, n]], {n, 2, 10000}]; t (* _T. D. Noe_, Oct 02 2013 *)
%Y Cf. A000045, A001175, A071774, A229467.
%K nonn
%O 1,1
%A _Matthew Goers_, Sep 24 2013
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