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 A126263 List of primes generated by factoring successive integers in Sylvester's sequence (A000058). 6
 2, 3, 7, 43, 13, 139, 3263443, 547, 607, 1033, 31051, 29881, 67003, 9119521, 6212157481, 5295435634831, 31401519357481261, 77366930214021991992277, 181, 1987, 112374829138729, 114152531605972711, 35874380272246624152764569191134894955972560447869169859142453622851 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The list is infinite and no term repeats since Sylvester's sequence is an infinite coprime sequence. However, it appears to be unknown if all terms in A000058 are squarefree. - Jeppe Stig Nielsen, Apr 23 2020 LINKS William Stein and Ray Chandler, Table of n, a(n) for n = 1..28 (first 27 terms from William Stein) J. K. Andersen, Factorization of Sylvester's sequence. Filip Saidak, Proof of Euclid's Theorem. Filip Saidak, A New Proof of Euclid's Theorem, Amer. Math. Monthly, Dec 2006 EXAMPLE 2 = 2, 3 = 3, 7 = 7, 43 = 43, 1807 = 13 * 139, 3263443 = 3263443, 10650056950807 = 547 * 607 * 1033 * 31051, 113423713055421844361000443 = 29881 * 67003 * 9119521 * 6212157481, 12864938683278671740537145998360961546653259485195807 = 5295435634831 * 31401519357481261 * 77366930214021991992277. 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443 = 181 * 1987 * 112374829138729 * 114152531605972711 * 35874380272246624152764569191134894955972560447869169859142453622851. - Jonathan Sondow, Jan 26 2014 MAPLE a(0):=2; for n from 0 to 8 do a(n+1):=a(n)^2-a(n)+1; ifactor(%); od; PROG (Sage) v = [2] for n in range(12):     v.append(v[-1]^2-v[-1]+1)     print(prime_divisors(v[-1])) # William Stein, Aug 26 2009 (PARI) v=[2]; for(i=1, 10, v=concat(v, Set(factor(vecprod(v)+1)[, 1]))); v \\ Charles R Greathouse IV, Oct 02 2014 CROSSREFS Cf. A000058, A007996, A236433. Sequence in context: A260819 A000945 A261564 * A323605 A216826 A030087 Adjacent sequences:  A126260 A126261 A126262 * A126264 A126265 A126266 KEYWORD nonn AUTHOR Howard L. Warth (hlw6c2(AT)umr.edu), Dec 22 2006 EXTENSIONS Offset corrected by N. J. A. Sloane, Aug 20 2009 a(23)-a(27) from William Stein (wstein(AT)gmail.com), Aug 20 2009, Aug 21 2009 a(17) corrected by D. S. McNeil, Dec 10 2010 b-file updated at suggestion of Hans Havermann by Ray Chandler, Feb 27 2015 STATUS approved

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Last modified April 21 15:48 EDT 2021. Contains 343154 sequences. (Running on oeis4.)