
COMMENTS

Cox and van der Poorten 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."


REFERENCES

C. Cobeli and A. Zaharescu, Promenade around Pascal TriangleNumber Motives, Bull. Math. Soc. Sci. Math. Roumanie, Tome 56(104) No. 1, 2013, 7398; http://rms.unibuc.ro/bulletin/pdf/561/PromenadePascalPart1.pdf.  From N. J. A. Sloane, Feb 16 2013
C. D. Cox and A. J. van der Poorten, On a sequence of prime numbers, Journal of the Australian Mathematical Society 8 (1968), pp. 571574.
R. K. Guy and R. Nowakowski, Discovering primes with Euclid, Delta (Waukesha), Vol. 5, pp. 4963, 1975.
Des MacHale, Infinitely many proofs that there are infinitely many primes, Math. Gazette, 97 (No. 540, 2013), 495498.
T. Naur, Mullin's sequence of primes is not monotonic, Proc. Amer. Math. Soc., 90 (1984), 4344.
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
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), 2332.


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}] (* Alonso del Arte, Jun 25 2011 based on the program given for A000945 *)
