0,2

Does this sequence grow indefinitely, or does it cycle? - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 02 2006

All a(n) except a(0) = 1 belong to A014442(n) = {2, 5, 5, 17, 13, 37, 5, 13, 41, 101, ...} Largest prime factor of n^2 + 1. All a(n) except a(0) = 1 belong to A002313(n) = {2, 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, ...} Primes congruent to 1 or 2 modulo 4; or, primes of form x^2+y^2; or, -1 is a square mod p. All a(n) except a(0) = 1 and a(1) = 2 are the Pythagorean primes A002144(n) = {5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, ...} Primes of form 4n+1. - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 05 2006

Dennis Langdeau, Table of n, a(n) for n = 0..24

Dario A. Alpern, Factorization: Elliptic Curve Method

Jason Papadopoulos, Integer Factorization Source Code.

a(16)=A006530(a(15)^2+1)=

A006530(101591133424866642486477019709^2+1)=

A006530(10320758390549056348725939119133160378521185060950774444682)=

A006530(2*29*23201*4645528280970018601*1650979973845742266714536305651329)=

1650979973845742266714536305651329, factorization of A006530(a(15)^2+1) by Dario A. Alpern's program (see link).

(PARI) gpf(n)=local(pf); pf=factor(n); pf[matsize(pf)[1], 1] vector(20, i, r=if(i==1, 1, gpf(r^2+1)))

Cf. A056650, A003095.

Cf. A002144 - Pythagorean primes: primes of form 4n+1. Cf. A002313 - Primes congruent to 1 or 2 modulo 4. cf. A014442 - Largest prime factor of n^2 + 1.

Adjacent sequences: A031436 A031437 A031438 this_sequence A031440 A031441 A031442

Sequence in context: A002313 A068486 A099332 this_sequence A074856 A087952 A124255

nonn,nice

Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp)

One more term from Vladeta Jovovic (vladeta(AT)Eunet.yu), Nov 26 2001

a(16) from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 07 2004

a(17)-a(21) from Richard FitzHugh (fitzhughrichard(AT)hotmail.com), Aug 12 2004