%I #12 Jun 07 2022 15:20:49

%S 13,41,29,109,2113,157,1321,26317,525313,1429,1657,268501,279073,

%T 536903681,49477,4327489,7416361,231769777,21841,43249589,500177,

%U 29247661,7484047069,19707683773,1326700741,586477649,3630105520141,275415303169,104399276341

%N Largest prime factor of 2^(2*n+1)+2^(n+1)+1.

%C 2^(2*n+1)+2^(n+1)+1 is a factor of 4^(2*n+1)+1.

%H Daniel Suteu, <a href="/A229768/b229768.txt">Table of n, a(n) for n = 1..547</a>

%e For n=10, 2^(2*n+1)+2^(n+1)+1 = 2099201 = 13*113*1429, so a(10)=1429.

%t Table[FactorInteger[2^(2n+1)+2^(n+1)+1][[-1,1]],{n,30}] (* _Harvey P. Dale_, Nov 03 2017 *)

%o (PARI) a(n) = {f=factor(2^(2*n+1)+2^(n+1)+1); f[matsize(f)[1],1]}

%Y Cf. A085601, A207262, A229747, A229767.

%K nonn

%O 1,1

%A _Colin Barker_, Sep 29 2013