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

1,1

Comments

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

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A078726 A019434 A164307 * A093179 A067387 A050922

Adjacent sequences: A125042 A125043 A125044 * A125046 A125047 A125048

Keyword

nonn

Author

Nick Hobson, Nov 18 2006

Status

approved