A325627 - OEIS

%I #10 Oct 25 2024 07:15:24

%S 2,5,13,89,233,1597,113,28657,514229,2417,2221,59369,433494437,

%T 2971215073,55945741,2710260697,555003497,1429913,46165371073,

%U 86020717,92180471494753,99194853094755497,1665088321800481,361040209,770857978613,512119709,8242065050061761

%N a(n) is the largest prime factor in A030426(n).

%H Amiram Eldar, <a href="/A325627/b325627.txt">Table of n, a(n) for n = 1..222</a>

%H C. L. Stewart, <a href="https://doi.org/10.1112/plms/s3-35.3.425">On Divisors of Fermat, Fibonacci, Lucas, and Lehmer Numbers</a>, Proceedings of the London Mathematical Society, Vol. s3-35, No. 3 (1977), pp. 425-447. See p. 430.

%F From _Amiram Eldar_, Oct 25 2024: (Start)

%F a(n) = A006530(A030426(n)).

%F a(n) = A060385(prime(n+1)).

%F a(n) > c * prime(n) * log(prime(n)), where c is an effectively computable positive constant (Stewart, 1977). (End)

%t Table[FactorInteger[Fibonacci [Prime[n]]][[-1, 1]], {n, 2, 30}]

%o (Magma) [Maximum(PrimeDivisors(Fibonacci(NthPrime(n)))): n in [2..35]];

%Y Cf. A000045, A005478, A006530, A030426, A060385, A325626.

%K nonn

%O 1,1

%A _Vincenzo Librandi_, May 13 2019