A264137 Largest prime factor of the n-th Pell number, A000129(n).

2, 5, 3, 29, 7, 13, 17, 197, 41, 5741, 11, 33461, 239, 269, 577, 8297, 199, 179057, 59, 45697, 5741, 982789, 1153, 29201, 33461, 146449, 337, 44560482149, 269, 3272609, 665857, 52734529, 15607, 1800193921, 199, 1101341, 9369319, 4605197, 5521, 1746860020068409

Offset: 2

Author

Jon E. Schoenfield, Dec 29 2015

Keywords

• nonn

Comments

First differs from A246556 at n = 17. Since Pell(17) = 1136689 = 137 * 8297, we find that 137 does not divide any earlier Pell number, and hence A246556(17) = 137, but 8297 is also prime, and so a(17) = 8297.

Links

• Daniel Suteu and Jon E. Schoenfield, Table of n, a(n) for n = 2..630 (terms a(2)..a(240) from Jon E. Schoenfield)

Crossrefs

Cf. A000129, A006530, A060385, A246556.

Programs

Mathematica

Table[FactorInteger[Fibonacci[n, 2]][[-1, 1]], {n, 25}] (* Alonso del Arte, Dec 10 2016 *)
FactorInteger[#][[-1,1]]&/@LinearRecurrence[{2,1},{2,5},60] (* Harvey P. Dale, Jun 08 2019 *)

PARI

a(n) = vecmax(factor(([2, 1; 1, 0]^n)[2, 1])[,1]); \\ Daniel Suteu, May 26 2022

Formula

a(n) = A006530(A000129(n)).