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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.

%I A344258 #19 Jan 05 2025 19:51:42
%S A344258 4,11,15,19,21,29,31,35,39,51,59,69,71,79,91,101,111,115,119,131,139,
%T A344258 141,151,159,179,181,183,191,199,205,211,215,219,229,235,239,251,259,
%U A344258 267,271,287,291,299,301,309,311,327,329,331,335,339,349,359,371,379,381
%N 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.
%C A344258 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).
%H A344258 Patrick Flanagan, Marc S. Renault, and Josh Updike, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/53-1/FlanaganRenaultUpdike06032014.pdf">Symmetries of Fibonacci Points, Mod m</a>, Fibonacci Quart. 53 (2015), no. 1, 34-41. See p. 5.
%o A344258 (PARI) \\ where pisano(n) is A001175
%o A344258 hasrot(m) = {if (m==2, return (1)); my(j=pisano(m)/2); my(vf = [fibonacci(j), fibonacci(j+1)]); Mod(vf, m) == [0, -1];}
%o A344258 isok(m) = {if ((m>1) && !hasrot(m), fordiv(m, d, if ((d>1) && (d<m), if (!hasrot(d), return (0)))); return(1););}
%Y A344258 Cf. A000045, A001175, A275124, A344281.
%K A344258 nonn
%O A344258 1,1
%A A344258 _Michel Marcus_, May 13 2021