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%I
%S 2,3,7,43,13,139,3263443,547,607,1033,31051,29881,67003,9119521,
%T 6212157481,5295435634831,31401519357481261,77366930214021991992277,
%U 181,1987,112374829138729,114152531605972711
%N List of primes generated by factoring successive integers in Sylvester's sequence (A000058).
%C The list is infinite and no term repeats since Sylvester's sequence is an infinite coprime sequence.
%D F. Saidak, A New Proof of Euclid's Theorem, American Mathematical Monthly, December 2006
%H William Stein, <a href="/A126263/b126263.txt">Table of n, a(n) for n = 1..27</a>
%H Filip Saidak, <a href="http://primes.utm.edu/notes/proofs/infinite/Saidak.html">Proof of Euclid's Theorem</a>.
%p a(0):=2; for n from 0 to 8 do a(n+1):=a(n)^2-a(n)+1;ifactor(%); od;
%o (sage program from William Stein, Aug 26 2009)
%o v=[2]
%o for n in range(12):
%o ... v.append(v[-1]^2-v[-1]+1)
%o ... print prime_divisors(v[-1])
%o [2, 3, 7, 43, 13, 139, 3263443, 547, 607, 1033, 31051, 29881, 67003, 9119521, 6212157481, 5295435634831, 31401519357481261, 77366930214021991992277]
%Y Cf. A000058.
%K nonn
%O 1,1
%A Howard L. Warth (hlw6c2(AT)umr.edu), Dec 22 2006
%E Offset corrected by _N. J. A. Sloane_, Aug 20 2009
%E a(23) - a(27) from William Stein (wstein(AT)gmail.com), Aug 20 2009, Aug 21 2009
%E a(17) corrected by _D. S. McNeil_, Dec 10 2010
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