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.

2, 3, 5, 29, 79, 68729, 3739, 6221191, 157170297801581, 70724343608203457341903, 46316297682014731387158877659877, 78592684042614093322289223662773, 181891012640244955605725966274974474087, 547275580337664165337990140111772164867508038795347198579326533639132704344301831464707648235639448747816483406685904347568344407941

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..14.

Dario Alpern, Factorization using the Elliptic Curve Method

Example

a(4)=29 since 2*3*5=30 and 29 is the largest prime factor of 30-1
a(5)=79 since 2*3*5*29=870 and 79 is the largest prime factor of 870-1=869=11*79.

Crossrefs

Cf. A000946, A005265, A084598.

Essentially the same as A005266.

Sequence in context: A019400 A354084 A331399 * A062167 A358896 A279189

Adjacent sequences: A084596 A084597 A084598 * A084600 A084601 A084602

Keyword

nonn

Author

Marc LeBrun, May 31 2003

Extensions

More terms from Hugo Pfoertner, May 31, 2003, using Dario Alpern's ECM.

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.

Status

approved