A344258 Integers m for which F (mod m) does not have rotational symmetry although F (mod k) does have rotational symmetry for all factors k of m.

4, 11, 15, 19, 21, 29, 31, 35, 39, 51, 59, 69, 71, 79, 91, 101, 111, 115, 119, 131, 139, 141, 151, 159, 179, 181, 183, 191, 199, 205, 211, 215, 219, 229, 235, 239, 251, 259, 267, 271, 287, 291, 299, 301, 309, 311, 327, 329, 331, 335, 339, 349, 359, 371, 379, 381

Offset: 1

Author

Michel Marcus, May 13 2021

Keywords

• nonn

Comments

Flanagan et al. define F (mod m) as the set of points [x_i, y_i] (mod m) where x_i = Fibonacci(i) and y_i = Fibonacci(i+1).

Links

• Patrick Flanagan, Marc S. Renault, and Josh Updike, Symmetries of Fibonacci Points, Mod m, Fibonacci Quart. 53 (2015), no. 1, 34-41. See p. 5.

Crossrefs

Cf. A000045, A001175, A275124, A344281.

Programs

PARI

\\ where pisano(n) is A001175
hasrot(m) = {if (m==2, return (1)); my(j=pisano(m)/2); my(vf = [fibonacci(j), fibonacci(j+1)]); Mod(vf, m) == [0, -1];}
isok(m) = {if ((m>1) && !hasrot(m), fordiv(m, d, if ((d>1) && (d