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

Author

Carl R. White, Oct 05 2009

Keywords

• easy
• nonn

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

• Eric Weisstein's World of Mathematics, Pisano period.
• Wikipedia, Pisano period.

Crossrefs

Cf. A001175, A022405, A046738.

Programs

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"