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%I A084599 #9 Jul 08 2023 14:14:20
%S A084599 2,3,5,29,79,68729,3739,6221191,157170297801581,
%T A084599 70724343608203457341903,46316297682014731387158877659877,
%U A084599 78592684042614093322289223662773,181891012640244955605725966274974474087,547275580337664165337990140111772164867508038795347198579326533639132704344301831464707648235639448747816483406685904347568344407941
%N A084599 a(1) = 2, a(2) = 3; for n >= 2, a(n+1) is largest prime factor of (Product_{k=1..n} a(k)) - 1.
%C A084599 Like the Euclid-Mullin sequence A000946, but subtracting rather than adding 1 to the product.
%H A084599 Dario Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>
%e A084599 a(4)=29 since 2*3*5=30 and 29 is the largest prime factor of 30-1
%e A084599 a(5)=79 since 2*3*5*29=870 and 79 is the largest prime factor of 870-1=869=11*79.
%Y A084599 Cf. A000946, A005265, A084598.
%Y A084599 Essentially the same as A005266.
%K A084599 nonn
%O A084599 1,1
%A A084599 _Marc LeBrun_, May 31 2003
%E A084599 More terms from _Hugo Pfoertner_, May 31, 2003, using Dario Alpern's ECM.
%E A084599 The next term a(15) is not known. It requires the factorization of the 245-digit composite number which remains after eliminating 7 smaller factors.

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