A367420 Numbers k with the property that if a Fibonacci number f is divisible by k then f is also divisible by 2*k.

4, 6, 9, 12, 14, 17, 18, 19, 20, 22, 23, 24, 27, 28, 30, 31, 36, 38, 42, 44, 45, 46, 51, 52, 53, 54, 56, 57, 58, 60, 61, 62, 63, 66, 68, 69, 70, 72, 76, 78, 79, 81, 82, 83, 84, 85, 86, 90, 92, 93, 94, 95, 98, 99, 100, 102, 107, 108, 109, 110, 112, 114, 115, 116, 117

Offset: 1

Author

J. Lowell, Nov 17 2023

Keywords

• nonn

Comments

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

Examples

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

Links

• Robin Visser, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A001177.

Programs

Python

def is_A367420(k):
    a, b = 1, 1
    while((a,b)!=(0,1)):
        if (a==k): return False
        a, b = b, (a+b)%(2*k)
    return True
print([k for k in range(1, 1000) if is_A367420(k)])  # Robin Visser, Jan 08 2024

Extensions

More terms from David A. Corneth, Nov 17 2023