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%I #17 Jun 21 2022 18:30:51
%S 2,3,11,41,17,97,3137,13499,60741001,14158633,7424699571433,
%T 18375387908679124623224497,152868746152697352174823427,
%U 114585848725150699093848122619332057,2117552824725684501808097956698634897,34759922213207174486822944687721824905112848905750167403101021576017059,57191433705834025254780615830990723253902440879104281100230506839641
%N a(1) = 2, then a(n) = greatest prime factor of (a(n-1)^2+2).
%D Teske, Edlyn and Williams, Hugh C., A note on Shanks's chains of primes, in Algorithmic number theory (Leiden, 2000), 563-580, Lecture Notes in Comput. Sci., 1838, Springer, Berlin, 2000.
%H Dennis Langdeau, <a href="/A081173/b081173.txt">Table of n, a(n) for n = 1..20</a>
%e a(2) = 3 because 3 is greatest prime factor of 2^2+2. a(3)=11 because 3^2+2 is prime.
%t a[1]=2; a[n_] := a[n]=FactorInteger[a[n-1]^2+2][[ -1, 1]]
%t NestList[FactorInteger[#^2+2][[-1,1]]&,2,15] (* _Harvey P. Dale_, Jun 21 2022 *)
%Y Cf. A083388.
%K nonn
%O 1,1
%A _Donald S. McDonald_, Apr 17 2003
%E More terms from _Donald S. McDonald_, Apr 20 2003
%E More terms from _Robert G. Wilson v_ and _Dean Hickerson_, Apr 22 2003
%E More terms from Dennis Langdeau (dlangdea(AT)sfu.ca), Jun 18 2006
%E Definition clarified by _Harvey P. Dale_, Jun 21 2022