A361520 - OEIS

A361520

a(n) is the greatest prime factor of a(n-2)^2 + a(n-1)^2 where a(1)=2 and a(2)=3.

%I #40 May 07 2023 14:55:20

%S 2,3,13,89,809,349,409,144541,10446133981,1361264878245241,

%T 4398505263882824939701,17847523009215848981,

%U 512996953133650208042047593649109478833

%N a(n) is the greatest prime factor of a(n-2)^2 + a(n-1)^2 where a(1)=2 and a(2)=3.

%H Sebastian F. Orellana, <a href="/A361520/b361520.txt">Table of n, a(n) for n = 1..15</a>

%p A[1]:= 2: A[2]:= 3:

%p for n from 3 to 15 do A[n]:= max(numtheory:-factorset(A[n-2]^2 + A[n-1]^2)) od:

%p seq(A[],n=1..15); # _Robert Israel_, Mar 17 2023

%t a[1] = 2; a[2] = 3; a[n_] := a[n] = FactorInteger[a[n - 1]^2 + a[n - 2]^2][[-1, 1]]; Array[a, 14] (* _Amiram Eldar_, Mar 14 2023 *)

%Y Cf. A006530, A113494, A175723.

%K nonn

%O 1,1

%A _Sebastian F. Orellana_, Mar 14 2023