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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.

%I A125045 #22 Feb 11 2024 14:19:19
%S A125045 3,5,17,257,65537,641,7,318811,19,1747,12791,73,90679,67,59,113,13,41,
%T A125045 47,151,131,1301297155768795368671,20921,
%U A125045 1514878040967313829436066877903,5514151389810781513,283,1063,3027041,29,24040758847310589568111822987,154351,89
%N 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.
%C A125045 The first five terms comprise the known Fermat primes: A019434.
%H A125045 Sean A. Irvine, <a href="/A125045/b125045.txt">Table of n, a(n) for n = 1..64</a>
%e A125045 a(7) = 7 is the smallest prime divisor of 3 * 5 * 17 * 257 * 65537 * 641 + 2 = 2753074036097 = 7 * 11 * 37 * 966329953.
%t A125045 a={3}; q=1;
%t A125045 For[n=2,n<=20,n++,
%t A125045     q=q*Last[a];
%t A125045     AppendTo[a,Min[FactorInteger[q+2][[All,1]]]];
%t A125045     ];
%t A125045 a (* _Robert Price_, Jul 16 2015 *)
%Y A125045 Cf. A000945, A019434, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
%K A125045 nonn
%O A125045 1,1
%A A125045 _Nick Hobson_, Nov 18 2006