A084599 - OEIS

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.

%I #9 Jul 08 2023 14:14:20

%S 2,3,5,29,79,68729,3739,6221191,157170297801581,

%T 70724343608203457341903,46316297682014731387158877659877,

%U 78592684042614093322289223662773,181891012640244955605725966274974474087,547275580337664165337990140111772164867508038795347198579326533639132704344301831464707648235639448747816483406685904347568344407941

%N 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 Like the Euclid-Mullin sequence A000946, but subtracting rather than adding 1 to the product.

%H Dario Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>

%e a(4)=29 since 2*3*5=30 and 29 is the largest prime factor of 30-1

%e a(5)=79 since 2*3*5*29=870 and 79 is the largest prime factor of 870-1=869=11*79.

%Y Cf. A000946, A005265, A084598.

%Y Essentially the same as A005266.

%K nonn

%O 1,1

%A _Marc LeBrun_, May 31 2003

%E More terms from _Hugo Pfoertner_, May 31, 2003, using Dario Alpern's ECM.

%E 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.