A121169 Largest prime divisor of Fibonacci(100*n).

570601, 5738108801, 87129547172401, 3160438834174817356001, 158414167964045700001, 87129547172401, 7358192362316341243805801, 7601587101128729489773008667804801, 427694148584338087778220001

Offset: 1

Author

Alexander Adamchuk, Aug 14 2006

Keywords

• nonn

Comments

Most prime divisors of Fibonacci(100*n) are congruent to 1 mod 10 (final digit is 1). It appears that a(n) == 1 (mod 100) for all n.

Examples

			a(1) = 570601 because F(100) = 3 * 5^2 * 11 * 41 * 101 * 151 * 401 * 3001 * 570601.
a(10) = 9372625568572722938847095612481183137496995522804466421273200001 because F(1000)= 3 * 5^3 * 7 * 11 * 41 * 101 * 151 * 251 * 401 * 2161 * 3001 * 4001 * 570601 * 9125201 * 112128001 * 1353439001 * 5738108801 * 28143378001 * 5465167948001 * 10496059430146001 * 84817574770589638001 * 158414167964045700001 * 9372625568572722938847095612481183137496995522804466421273200001.
		

Crossrefs

Cf. A000045, A060385.

Programs

Mathematica

Table[Max[Flatten[FactorInteger[Fibonacci[100n]]]],{n,10}]

PARI

a(n) = my(f=factor(fibonacci(100*n))[, 1]); f[#f]; \\ Jinyuan Wang, Mar 17 2020

Formula

a(n) = A060385(100*n).