OFFSET
2,1
COMMENTS
First differs from A264137 (Largest prime factor of the n-th Pell number) at n=17; see Example section. - Jon E. Schoenfield, Dec 10 2016
LINKS
R. D. Carmichael, On the numerical factors of the arithmetic forms α^n ± β^n, Annals of Math., 15 (1/4) (1913), 30-70.
FORMULA
a(n) >= 2 for all n >= 2, by Carmichael's theorem. - Jonathan Sondow, Dec 08 2017
EXAMPLE
a(2) = 2 because Pell(2) = 2 and Pell(k) < 2 for k < 2.
a(4) = 3 because Pell(4) = 12 = 2^2 * 3, but 2 is not a primitive prime factor since Pell(2) = 2, so therefore 3 is the primitive prime factor.
a(5) = 29 because Pell(5) = 29, which is prime.
a(6) = 7 because Pell(6) = 70 = 2 * 5 * 7, but neither 2 nor 5 is a primitive prime factor, so therefore 7 is the primitive prime factor.
a(17) = 137 because Pell(17) = 1136689 = 137 * 8297, and both of them are primitive factors, we choose the smallest. (Pell(17) is the smallest Pell number with more than one primitive prime factor.)
MATHEMATICA
prms={}; Table[f=First/@FactorInteger[Pell[n]]; p=Complement[f, prms]; prms=Join[prms, p]; If[p=={}, 1, First[p]], {n, 36}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Chen, Nov 15 2014
EXTENSIONS
Edited by N. J. A. Sloane, Nov 29 2014
Terms up to a(612) in b-file added by Sean A. Irvine, Sep 23 2019
Terms a(613)-a(630) in b-file added by Max Alekseyev, Aug 26 2021
STATUS
approved