%I A005266 M2247
%S A005266 3,2,5,29,79,68729,3739,6221191,157170297801581,70724343608203457341903,
%T A005266 46316297682014731387158877659877,78592684042614093322289223662773,181891012640244955605725966274974474087,
%U A005266 5472755803376641653379901401117721648675080387953471985793265336391327043443018314647076482356394487478164834\
               06685904347568344407941
%N A005266 a(1)=3, b(n)=Product_{k=1..n} a(k), a(n+1)=largest prime factor of b(n)-1.
%C A005266 Suggested by Euclid's proof that there are infinitely many primes.
%C A005266 a(15) requires completing the factorization: 13 * 67 * 14479 * 167197 
               * 924769 * 2688244927 * 888838110930755119 * 14372541055015356634061816579965403 
               * C211 where C211=660913330662648363444866649464673779962464061606073030214218754540558253101039029050200\
               115688391702320267155451063346004790145995995932534247513277879149511293756294106652390760328158679687633\
               5607258627832127303 [From Sean A. Irvine (sairvin(AT)xtra.co.nz), 
               Nov 10 2009]
%D A005266 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005266 R. K. Guy and R. Nowakowski, Discovering primes with Euclid, Delta (Waukesha), 
               Vol. 5, pp. 49-63, 1975.
%D A005266 S. S. Wagstaff, Jr., Computing Euclid's primes, Bull. Institute Combin. 
               Applications, 8 (1993), 23-32.
%Y A005266 Cf. A000945, A000946, A005265.
%Y A005266 Essentially the same as A084599.
%Y A005266 Sequence in context: A103938 A085973 A005265 this_sequence A005267 A016460 
               A097887
%Y A005266 Adjacent sequences: A005263 A005264 A005265 this_sequence A005267 A005268 
               A005269
%K A005266 nonn,nice,new
%O A005266 0,1
%A A005266 N. J. A. Sloane (njas(AT)research.att.com).
%E A005266 a(14) from Joe K. Crump (joecr(AT)carolina.rr.com), Jul 26, 2000