%I A000945 M0863 N0329
%S A000945 2,3,7,43,13,53,5,6221671,38709183810571,139,2801,11,17,5471,52662739,
%T A000945 23003,30693651606209,37,1741,1313797957,887,71,7127,109,23,97,159227,
               643679794963466223081509857,
%U A000945 103,1079990819,9539,3143065813,29,3847,89,19,577,223,139703,457,9649,
               61,4357
%N A000945 Euclid-Mullin sequence: a(1) = 2, a(n+1) is smallest prime factor of 
               Product_{k=1..n} a(k) + 1.
%C A000945 "Does the sequence ... contain every prime? ... [It] was considered by 
               Guy and Nowakowski and later by Shanks, [Wagstaff 1993] computed 
               the sequence through the 43rd term. The computational problem inherent 
               in continuing the sequence further is the enormous size of the numbers 
               that must be factored. Already the number a(1)* ... *a(43) + 1 has 
               180 digits." - Crandall and Pomerance.
%C A000945 If this variant of Euclid-Mullin sequence is initiated either with 3, 
               7 or 43 instead of 2, then from a[5] onwards it is unchanged. See 
               also A051614. - Labos E. (labos(AT)ana.sote.hu), May 03 2004
%D A000945 R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, 
               Springer, NY, 2001; see p. 6.
%D A000945 R. K. Guy and R. Nowakowski, Discovering primes with Euclid, Delta (Waukesha), 
               Vol. 5, pp. 49-63, 1975.
%D A000945 A. A. Mullin, Recursive function theory, Bull. Amer. Math. Soc., 69 (1963), 
               737.
%D A000945 T. Naur, Mullin's sequence of primes is not monotonic, Proc. Amer. Math. 
               Soc., 90 (1984), 43-44.
%D A000945 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000945 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000945 S. S. Wagstaff, Jr., Computing Euclid's primes, Bull. Institute Combin. 
               Applications, 8 (1993), 23-32.
%e A000945 a(5) is equal to 13 because 2*3*7*43+1 = 1807 = 13 * 139.
%t A000945 f[1]=2; f[n_] := f[n] = FactorInteger[Product[f[i], {i, 1, n - 1}] + 
               1][[1, 1]] Table[f[n], {n, 1, 46}]
%Y A000945 Cf. A000946, A005265, A005266.
%Y A000945 Cf. A051309-A051334, A051614, A051614-A051616, A056756.
%Y A000945 Sequence in context: A102604 A119662 A163157 this_sequence A126263 A030087 
               A106864
%Y A000945 Adjacent sequences: A000942 A000943 A000944 this_sequence A000946 A000947 
               A000948
%K A000945 nonn,nice,hard
%O A000945 1,1
%A A000945 N. J. A. Sloane (njas(AT)research.att.com).