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 A000946 Euclid-Mullin sequence: a(1) = 2, a(n+1) is largest prime factor of Product_{k=1..n} a(k) + 1. (Formerly M0864 N0330) 42

%I M0864 N0330

%S 2,3,7,43,139,50207,340999,2365347734339,4680225641471129,

%T 1368845206580129,889340324577880670089824574922371,

%U 20766142440959799312827873190033784610984957267051218394040721

%N Euclid-Mullin sequence: a(1) = 2, a(n+1) is largest prime factor of Product_{k=1..n} a(k) + 1.

%C Cox and van der Poorten show that 5, 11, 13, 17, ... are not members of this sequence. - _Charles R Greathouse IV_, Jul 02 2007

%C Booker's abstract claims: "We consider the second of Mullin's sequences of prime numbers related to Euclid's proof that there are infinitely many primes. We show in particular that it omits infinitely many primes, confirming a conjecture of Cox and van der Poorten."

%D C. Cobeli and A. Zaharescu, Promenade around Pascal Triangle-Number Motives, Bull. Math. Soc. Sci. Math. Roumanie, Tome 56(104) No. 1, 2013, 73-98; http://rms.unibuc.ro/bulletin/pdf/56-1/PromenadePascalPart1.pdf. - From _N. J. A. Sloane_, Feb 16 2013

%D C. D. Cox and A. J. van der Poorten, On a sequence of prime numbers, Journal of the Australian Mathematical Society 8 (1968), pp. 571-574.

%D R. K. Guy and R. Nowakowski, Discovering primes with Euclid, Delta (Waukesha), Vol. 5, pp. 49-63, 1975.

%D R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, Arxiv preprint arXiv:1202.3670, 2012 - From _N. J. A. Sloane_, Jun 13 2012

%D T. Naur, Mullin's sequence of primes is not monotonic, Proc. Amer. Math. Soc., 90 (1984), 43-44.

%D P. Pollack and E. Trevino, The primes that Euclid forgot, http://www.math.uga.edu/~pollack/mullin.pdf, 2013. - From _N. J. A. Sloane_, Feb 20 2013

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D S. S. Wagstaff, Jr., Computing Euclid's primes, Bull. Institute Combin. Applications, 8 (1993), 23-32.

%H T. D. Noe, <a href="/A000946/b000946.txt">Table of n, a(n) for n = 1..14</a>

%H Andrew R. Booker, <a href="http://www.integers-ejcnt.org/vol12a.html">On Mullin's second sequence of primes</a>, Integers, 12A (2012), article A4.

%H Mersenne Forum, <a href="http://mersenneforum.org/showthread.php?t=17884">The second Euclid-Mullin sequence</a>

%t f[1] = 2; f[n_] := f[n] = FactorInteger[Product[f[i], {i, 1, n - 1}] + 1][[-1, 1]]; Table[f[n], {n, 1, 10}] (* From Alonso del Arte, Jun 25 2011 based on the program given for A000945 *)

%Y Cf. A000945, A005265, A005266.

%K nonn,nice

%O 1,1

%A _N. J. A. Sloane_.

%E Extended by _Andrew R. Booker_, Mar 13 2013

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