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A121169 Largest prime divisor of Fibonacci(100*n). 1

%I #10 Oct 15 2023 18:58:31

%S 570601,5738108801,87129547172401,3160438834174817356001,

%T 158414167964045700001,87129547172401,7358192362316341243805801,

%U 7601587101128729489773008667804801,427694148584338087778220001

%N Largest prime divisor of Fibonacci(100*n).

%C 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.

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

%e a(1) = 570601 because F(100) = 3 * 5^2 * 11 * 41 * 101 * 151 * 401 * 3001 * 570601.

%e 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.

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

%o (PARI) a(n) = my(f=factor(fibonacci(100*n))[, 1]); f[#f]; \\ _Jinyuan Wang_, Mar 17 2020

%Y Cf. A000045, A060385.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Aug 14 2006

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Last modified April 17 08:54 EDT 2024. Contains 371763 sequences. (Running on oeis4.)