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

1,11

Links

Table of n, a(n) for n=1..79.

Formula

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

Prog

(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

Crossrefs

Cf. A343722.

Sequence in context: A375108 A373924 A028928 * A260149 A091379 A151758

Adjacent sequences: A343720 A343721 A343722 * A343724 A343725 A343726

Keyword

nonn

Author

Jon E. Schoenfield, May 02 2021

Status

approved