A367420 - OEIS

%I #36 Jan 08 2024 22:38:55

%S 4,6,9,12,14,17,18,19,20,22,23,24,27,28,30,31,36,38,42,44,45,46,51,52,

%T 53,54,56,57,58,60,61,62,63,66,68,69,70,72,76,78,79,81,82,83,84,85,86,

%U 90,92,93,94,95,98,99,100,102,107,108,109,110,112,114,115,116,117

%N Numbers k with the property that if a Fibonacci number f is divisible by k then f is also divisible by 2*k.

%C If k is a term then so is b*k for any odd b.

%H Robin Visser, <a href="/A367420/b367420.txt">Table of n, a(n) for n = 1..10000</a>

%e 4 is in the sequence as any Fibonacci number divisible by 4 is divisible by 2*4.

%o (Python)

%o def is_A367420(k):

%o     a, b = 1, 1

%o     while((a,b)!=(0,1)):

%o         if (a==k): return False

%o         a, b = b, (a+b)%(2*k)

%o     return True

%o print([k for k in range(1, 1000) if is_A367420(k)])  # _Robin Visser_, Jan 08 2024

%Y Cf. A000045, A001177.

%K nonn

%O 1,1

%A _J. Lowell_, Nov 17 2023

%E More terms from _David A. Corneth_, Nov 17 2023