A074214 Integers m such that F(m) and F(2m) have the same largest prime factor where F(k) denotes the k-th Fibonacci number.

3, 15, 21, 23, 25, 29, 33, 35, 39, 43, 45, 51, 55, 59, 63, 65, 75, 82, 83, 85, 87, 93, 99, 105, 107, 109, 111, 115, 119, 123, 125, 127, 131, 132, 133, 135, 137, 139, 142, 143, 145, 147, 151, 153, 158, 161, 166, 171, 173, 175, 179, 181, 183, 185, 187, 189, 191

Offset: 1

Author

Benoit Cloitre, Sep 17 2002

Keywords

• nonn

Comments

Why are even values rare? (First one is 82.)

Examples

			F(15) = 610 = 2*5*61 and F(30) = 832040 = 2^3*5*11*31*61 hence 15 is in the sequence.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..225

Crossrefs

Cf. A000045, A060385.

Programs

Mathematica

Select[Range[3,200],FactorInteger[Fibonacci[#]][[-1,1]]==FactorInteger[ Fibonacci[2#]][[-1,1]]&] (* Harvey P. Dale, Sep 04 2018 *)

PARI

f(n) = vecmax(factor(fibonacci(n))[,1]); \\ A060385
isok(m) = (m>2) && (f(m) == f(2*m)); \\ Michel Marcus, Feb 18 2021

Extensions

More terms from Don Reble, Sep 20 2002