A175289 Pisano period of A002605 modulo n.

1, 1, 3, 1, 24, 3, 48, 1, 9, 24, 10, 3, 12, 48, 24, 1, 144, 9, 180, 24, 48, 10, 22, 3, 120, 12, 27, 48, 840, 24, 320, 1, 30, 144, 48, 9, 36, 180, 12, 24, 280, 48, 308, 10, 72, 22, 46, 3, 336, 120, 144, 12, 936, 27, 120, 48, 180, 840, 29, 24, 60, 320, 144, 1, 24, 30, 1122, 144

Offset: 1

Author

R. J. Mathar, Mar 24 2010

Keywords

• nonn

Comments

a(79)=6240. [John W. Layman, Aug 10 2010]

Examples

			Reading 0, 1, 2, 6, 16, 44, 120, 328, 896, 2448,.. modulo 12 gives 0, 1, 2, 6, 4, 8, 0, 4, 8, 0, 4, 8 ,.. with period length a(n=12)= 3.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A001175, A046738, A175181, A175182, A175183, A175184, A175185, A175286.

Programs

Mathematica

a={1};For[n=2,n<=80,n++,{x={{0,1}}; t={1,1}; While[ !MemberQ[x,t], {xl = x[[ -1]]; AppendTo[x,t]; t={Mod[2*(t[[1]]+xl[[1]]),n], Mod[2*(t[[2]] + xl[[2]]),n]};}]; p = Flatten[Position[x,t]][[1]]; AppendTo[a, Length[x] - p+1];}]; Print[a]; (* John W. Layman, Aug 10 2010 *)

Extensions

Terms beyond a(28)=48 from John W. Layman, Aug 10 2010