OFFSET
1,2
COMMENTS
Numbers n such that A001175(n) (mod n) == 0.
FORMULA
Numbers of the form 2^a*5^b*6^c, b={0, 1, 2, ...}, c={0, 1} and a={0, 1, 2} but only equal 1 or 2 if b or c > 0. - Robert G. Wilson v
Equivalently, [1,6,10,12,20,24]*5^m, m>=0.
EXAMPLE
6 is in the list because the first 24 Fibonacci numbers (A000045) are:
0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657;
mod(Fibonacci(k=0..inf.), 6) is:
0,1,1,2,3,5,2,1,3,4,1,5,0,5,5,4,3,1,4,5,3,2,5,1 repeated;
this has period 24 which is a multiple of 6; therefore 6 is a member.
MATHEMATICA
f[n_] := Block[{a = a0 = {1, 0}, k = 0}, While[k++; s = Mod[Plus @@ a, n]; a = RotateLeft[a]; a[[2]] = s; a != a0]; k]; lst = {1}; Do[ If[ Mod[ f[n], n] == 0, AppendTo[lst, n]; Print[n]], {n, 2, 469000}] (* Robert G. Wilson v, May 31 2005 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
James Higham-Kessler (James_Higham-Kessler(AT)Brown.edu), Apr 27 2005
EXTENSIONS
Edited by Robert G. Wilson v, who also found a(30)-a(45), May 31 2005
STATUS
approved