User:Jaume Oliver Lafont/2^n mod N

2^n mod 3 A000034 period 2.

2^n mod 5 A070402 period 4, G.f.: (1+x+3*x^2)/((1-x)(1+x^2)); a(n)=(5-3*cos(n*Pi/2)-sin(n*Pi/2))/2

2^n mod 7 A069705 period 3; 3*2^n mod 7 is (3,6,5) period 3

2^n mod 11 A036117 period 10

2^n mod 13 A036118 period 12.

2^n mod 17 A062116 period 8, G.f.: (1+x+2*x^2+4*x^3+9*x^4)/(1-x)/(1+x^4), a(n)=17-a(n-4), a(n)=if(n%8<4,2^(n%4),17-2^(n%4)); 3*2^n mod 17 has period 8, G.f.: (3+3*x+6*x^2-5*x^3+10*x^4)/(1-x)/(1+x^4), a(n)=17-a(n-4), ---;

2^n mod 19 A036120 period 18.

2^n mod 23 A070335 period 11; 5*2^n mod 23 has period 11.