%I A005265 M2246
%S A005265 3,2,5,29,11,7,13,37,32222189,131,136013303998782209,31,197,19,157,
%T A005265 17,8609,1831129,35977,508326079288931,487,10253,1390043,18122659735201507243,
               25319167,9512386441,85577,1031,
%U A005265 3650460767,107,41,811,15787,89,68168743,4583,239,1283,443,902404933,64775657,
               2753,23,149287,149749,7895159,79,43,1409,184274081,47,569,63843643
%N A005265 a(1)=3, b(n)=Product_{k=1..n} a(k), a(n+1)=smallest prime factor of b(n)-1.
%C A005265 Suggested by Euclid's proof that there are infinitely many primes.
%D A005265 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005265 R. K. Guy and R. Nowakowski, ``Discovering primes with Euclid,'' Delta 
               (Waukesha), Vol. 5, pp. 49-63, 1975.
%D A005265 S. S. Wagstaff, Jr., Computing Euclid's primes, Bull. Institute Combin. 
               Applications, 8 (1993), 23-32.
%H A005265 Sean A. Irvine (sairvin(AT)xtra.co.nz) added terms 54 through 61, May 
               21 2006, giving <a href="b005265.txt">Table of n, a(n) for n = 1..61</
               a>
%Y A005265 Cf. A000945, A000946, A005266, A084599.
%Y A005265 Essentially the same as A084598.
%Y A005265 Sequence in context: A077039 A103938 A085973 this_sequence A005266 A005267 
               A016460
%Y A005265 Adjacent sequences: A005262 A005263 A005264 this_sequence A005266 A005267 
               A005268
%K A005265 nonn,nice
%O A005265 1,1
%A A005265 N. J. A. Sloane (njas(AT)research.att.com).