

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.


19



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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, A057204A057208, A051308A051335, A124984A124993, A125037A125045.
Sequence in context: A078726 A019434 A164307 * A093179 A067387 A050922
Adjacent sequences: A125042 A125043 A125044 * A125046 A125047 A125048


KEYWORD

nonn


AUTHOR

Nick Hobson (http://www.qbyte.org/puzzles/), Nov 18 2006


STATUS

approved



