A081173 a(1) = 2, then a(n) = greatest prime factor of (a(n-1)^2+2).

2, 3, 11, 41, 17, 97, 3137, 13499, 60741001, 14158633, 7424699571433, 18375387908679124623224497, 152868746152697352174823427, 114585848725150699093848122619332057, 2117552824725684501808097956698634897, 34759922213207174486822944687721824905112848905750167403101021576017059, 57191433705834025254780615830990723253902440879104281100230506839641

Offset: 1

Author

Donald S. McDonald, Apr 17 2003

Keywords

• nonn

Examples

			a(2) = 3 because 3 is greatest prime factor of 2^2+2. a(3)=11 because 3^2+2 is prime.
		

References

• 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.

Links

• Dennis Langdeau, Table of n, a(n) for n = 1..20

Crossrefs

Cf. A083388.

Programs

Mathematica

a[1]=2; a[n_] := a[n]=FactorInteger[a[n-1]^2+2][[ -1, 1]]
NestList[FactorInteger[#^2+2][[-1,1]]&,2,15] (* Harvey P. Dale, Jun 21 2022 *)

Extensions

More terms from Donald S. McDonald, Apr 20 2003

More terms from Robert G. Wilson v and Dean Hickerson, Apr 22 2003

More terms from Dennis Langdeau (dlangdea(AT)sfu.ca), Jun 18 2006

Definition clarified by Harvey P. Dale, Jun 21 2022