A125045 Odd primes generated recursively: a(1) = 3, a(n) = Min {p is prime; p divides Q+2}, where Q is the product of previous terms in the sequence.

3, 5, 17, 257, 65537, 641, 7, 318811, 19, 1747, 12791, 73, 90679, 67, 59, 113, 13, 41, 47, 151, 131, 1301297155768795368671, 20921, 1514878040967313829436066877903, 5514151389810781513, 283, 1063, 3027041, 29, 24040758847310589568111822987, 154351, 89

Offset: 1

Author

Nick Hobson, Nov 18 2006

Keywords

• nonn

Comments

The first five terms comprise the known Fermat primes: A019434.

Examples

			a(7) = 7 is the smallest prime divisor of 3 * 5 * 17 * 257 * 65537 * 641 + 2 = 2753074036097 = 7 * 11 * 37 * 966329953.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..64

Crossrefs

Cf. A000945, A019434, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

Programs

Mathematica

a={3}; q=1;
For[n=2,n<=20,n++,
    q=q*Last[a];
    AppendTo[a,Min[FactorInteger[q+2][[All,1]]]];
    ];
a (* Robert Price, Jul 16 2015 *)