A121170 Largest prime divisor of Fibonacci(5n).

5, 11, 61, 41, 3001, 61, 141961, 2161, 109441, 3001, 474541, 2521, 14736206161, 141961, 230686501, 3041, 3415914041, 109441, 67735001, 570601, 8288823481, 474541, 2441738887963981, 20641, 158414167964045700001, 14736206161, 1114769954367361, 12317523121, 349619996930737079890201

Offset: 1

Author

Alexander Adamchuk, Aug 14 2006

Keywords

• nonn

Comments

Except for a(1) = 5 all a(n) are congruent to 1 (mod 10) (final digit is 1). Final digit of most prime divisors of F(5n) is 1.

Examples

			a(2) = 11 because F(10)= 5 * 11.
a(4) = 41 because F(20)= 3 * 5 * 11 * 41.
a(10) = 3001 because F(50)= 5^2 * 11 * 101 * 151 * 3001.
a(25) = 158414167964045700001 because F(125)= 5^3 * 3001 * 158414167964045700001.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..284

Crossrefs

Cf. A000045, A060385.

Programs

Mathematica

Table[Max[Flatten[FactorInteger[Fibonacci[5n]]]],{n,1,50}]

Formula

a(n) = A060385(5*n).

Extensions

a(27)-a(29) from Amiram Eldar, Aug 01 2024