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

2,1

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)

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A000129, A006530, A060385, A246556.

Sequence in context: A122992 A051497 A246556 * A308949 A109734 A239309

Adjacent sequences: A264134 A264135 A264136 * A264138 A264139 A264140

Keyword

nonn

Author

Jon E. Schoenfield, Dec 29 2015

Status

approved