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A000946
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Euclid-Mullin sequence: a(1) = 2, a(n+1) is largest prime factor of Product_{k=1..n} a(k) + 1.
(Formerly M0864 N0330)
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39
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2, 3, 7, 43, 139, 50207, 340999, 2365347734339, 4680225641471129, 1368845206580129, 889340324577880670089824574922371, 20766142440959799312827873190033784610984957267051218394040721, 3486546133523738294549021453705017008734873145092643149204854821614266466998637603378972254923344607825545244648001799
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Cox and van der Poorten claim to show that 5, 11, 13, 17, ... are not members of this sequence. - Charles R Greathouse IV, Jul 02 2007
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."
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REFERENCES
| A. R. Booker, On Mullin's second sequence of primes, Arxiv preprint arXiv:1107.3318, 2011
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. [Note that the argument used here is incorrect, as pointed out by Naur.]
R. K. Guy and R. Nowakowski, Discovering primes with Euclid, Delta (Waukesha), Vol. 5, pp. 49-63, 1975.
T. Naur, Mullin's sequence of primes is not monotonic, Proc. Amer. Math. Soc., 90 (1984), 43-44.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. S. Wagstaff, Jr., Computing Euclid's primes, Bull. Institute Combin. Applications, 8 (1993), 23-32.
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LINKS
| Andrew R. Booker, On Mullin's second sequence of primes, July 17, 2011 [Jonathan Vos Post, July 18, 2011].
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MATHEMATICA
| 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 *)
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CROSSREFS
| Cf. A000945, A005265, A005266.
Sequence in context: A106864 A085682 A083369 * A091771 A072714 A051786
Adjacent sequences: A000943 A000944 A000945 * A000947 A000948 A000949
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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