A229466 Numbers k such that the period of Fibonacci numbers mod k is 3*(k+10).

10, 30, 70, 130, 370, 430, 670, 730, 970, 1030, 1270, 1570, 1630, 1930, 2230, 2770, 2830, 3130, 3370, 3670, 3730, 3970, 4330, 4570, 4630, 4870, 5230, 5470, 5770, 6070, 6130, 6430, 6730, 7270, 7330, 7570, 7870, 8230, 8530, 8770, 8830, 9070, 9370, 9970

Offset: 1

Author

Matthew Goers, Sep 24 2013

Keywords

• nonn

Comments

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.

Examples

			The Pisano period of the Fibonacci numbers mod 30 = 120, which is 3*(30+10).
The Pisano period of the Fibonacci numbers mod 1570 = 4740, which is 3*(1570+10).
		

Links

• Matthew Goers, Table of n, a(n) for n = 1..74

Crossrefs

Cf. A000045, A001175, A071774, A229467.

Programs

Mathematica

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 *)