%I A126263
%S A126263 2,3,7,43,13,139,3263443,547,607,1033,31051,29881,67003,9119521,
%T A126263 6212157481,5295435634831,31412519357481261,77366930214021991992277,181,
%U A126263 1987,112374829138729,114152531605972711
%N A126263 List of primes generated by factoring successive integers in Sylvester's 
               sequence (A000058).
%C A126263 The list is infinite and no term repeats since Sylvester's sequence is 
               an infinite coprime sequence.
%D A126263 F. Saidak, A New Proof of Euclid's Theorem, American Mathematical Monthly, 
               December 2006
%H A126263 William Stein, <a href="b126263.txt">Table of n, a(n) for n = 1..27</
               a>
%H A126263 Filip Saidak, <a href="http://primes.utm.edu/notes/proofs/infinite/Saidak.html">
               Proof of Euclid's Theorem</a>.
%p A126263 a(0):=2; for n from 0 to 8 do a(n+1):=a(n)^2-a(n)+1;ifactor(%); od;
%o A126263 (sage program from William Stein, Aug 26 2009)
%o A126263 v=[2]
%o A126263 for n in range(12):
%o A126263 ... v.append(v[-1]^2-v[-1]+1)
%o A126263 ... print prime_divisors(v[-1])
%o A126263 [2, 3, 7, 43, 13, 139, 3263443, 547, 607, 1033, 31051, 29881, 67003, 
               9119521, 6212157481, 5295435634831, 31401519357481261, 77366930214021991992277]
%Y A126263 Cf. A000058.
%Y A126263 Sequence in context: A119662 A163157 A000945 this_sequence A030087 A106864 
               A085682
%Y A126263 Adjacent sequences: A126260 A126261 A126262 this_sequence A126264 A126265 
               A126266
%K A126263 nonn
%O A126263 1,1
%A A126263 Howard L. Warth (hlw6c2(AT)umr.edu), Dec 22 2006
%E A126263 Offset corrected by N. J. A. Sloane, Aug 20 2009
%E A126263 a(23) - a(27) from William Stein (wstein(AT)gmail.com), Aug 20 2009, 
               Aug 21 2009