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

1,1

Comments

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

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000045, A060385.

Sequence in context: A048087 A316751 A001897 * A036897 A129966 A354675

Adjacent sequences: A074211 A074212 A074213 * A074215 A074216 A074217

Keyword

nonn

Author

Benoit Cloitre, Sep 17 2002

Extensions

More terms from Don Reble, Sep 20 2002

Status

approved