A084598 a(1) = 2, a(2) = 3; for n >= 2, a(n+1) is smallest prime factor of (Product_{k = 1..n} a(k)) - 1.

2, 3, 5, 29, 11, 7, 13, 37, 32222189, 131, 136013303998782209, 31, 197, 19, 157, 17, 8609, 1831129, 35977, 508326079288931, 487, 10253, 1390043, 18122659735201507243, 25319167, 9512386441, 85577, 1031, 3650460767, 107

Offset: 1

Author

Marc LeBrun, May 31 2003

Keywords

• nonn

Comments

Like the Euclid-Mullin sequence A000945, but subtracting rather than adding 1 to the product.

The first 4 terms are identical with A084599. It starts diverging at a(5) because the factorization of 2*3*5*29 - 1 = 869 = 11*79 gives A084598(5)=11 and A084599(5)=79. - Hugo Pfoertner, Mar 31 2004

Examples

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

Links

• Sean A. Irvine added terms 54 through 61, May 21 2006, giving Table of n, a(n) for n = 1..61
• Dario Alpern, Factorization using the Elliptic Curve Method

Crossrefs

Cf. A000945, A005266, A084598, A084599.

Essentially the same as A005265.

Programs

Mathematica

a={2,3}; q=2;
For[n=3,n<=19,n++,
    q=q*Last[a];
    AppendTo[a,Min[FactorInteger[q-1][[All,1]]]];
    ];
a (* Robert Price, Jul 17 2015 *)

Extensions

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