A166038 Period of A022405 mod n.

1, 3, 12, 18, 30, 12, 42, 18, 24, 30, 48, 36, 42, 42, 60, 36, 102, 24, 78, 90, 84, 48, 24, 36, 30, 42, 72, 126, 84, 60, 312, 72, 48, 102, 210, 72, 84, 78, 84, 90, 48, 84, 66, 144, 120, 24, 18, 36, 42, 30, 204, 126, 276, 72, 240, 126, 156, 84, 144, 180, 444, 312, 168, 144

Offset

1,2

Comments

Pisano-style numbers for the recurrence b(n) = n for 0 <= n <= 2, otherwise b(n) = b(n-1)*b(n-2) - b(n-3); that is, the sequence b(n) = A022405(n+1).

Links

Table of n, a(n) for n=1..64.

Eric Weisstein's World of Mathematics, Pisano period.

Wikipedia, Pisano period.

Prog

(bc) /* GNU bc */ define p(m){auto os, a, b, c, d, k; if(m<3)return 2*m-1; os=scale; scale=0; a=0; b=1; c=2; k=0; while(1){d=(c*b+m-a)%m; a=b; b=c; c=d; k+=1; if(a==0&&b==1&&c==2)break}; scale=os; return k}; for(i=1; i<=200; i++)print p(i), ", "; print"\n"

Crossrefs

Cf. A001175, A022405, A046738.

Sequence in context: A061564 A348169 A342785 * A052637 A120623 A158517

Adjacent sequences: A166035 A166036 A166037 * A166039 A166040 A166041

Keyword

easy,nonn

Author

Carl R. White, Oct 05 2009

Status

approved