A125045 - OEIS

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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

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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++,