A343723 a(n) is 1/4 of the number of starting residues r modulo n from which repeated iterations of the mapping r -> r^2 mod n never reach a fixed point.

0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 4, 0, 3, 4, 5, 0, 4, 4, 4, 4, 6, 0, 7, 0, 6, 0, 5, 4, 8, 8, 6, 0, 8, 6, 10, 8, 5, 10, 11, 0, 10, 8, 0, 8, 12, 8, 10, 8, 12, 12, 14, 0, 14, 14, 12, 0, 10, 12, 16, 0, 15, 10, 17, 8, 16, 16, 12, 16, 17, 12, 19

Offset: 1

Author

Jon E. Schoenfield, May 02 2021

Keywords

• nonn

Crossrefs

Cf. A343722.

Programs

PARI

pos(list, r) = forstep (k=#list, 1, -1, if (list[k] == r, return (#list - k + 1)););
isok(r, n) = {my(list = List()); listput(list, r); for (k=1, oo, r = lift(Mod(r, n)^2); my(i = pos(list, r)); if (i==1, return (1)); if (i>1, return(0)); listput(list, r); );}
a(n) = sum(r=0, n-1, 1 - isok(r, n))/4; \\ Michel Marcus, May 02 2021

Formula

a(n) = A343722(n)/4.