need more terms for A084598 & A084599

mlb at mlb at
Sat May 31 20:33:49 CEST 2003

I just submitted A084598 & A084599, which unfortunately match for the first
15 terms I was able to quickly calculate!  Any help extending these, especially
to their point of divergence, will be greatly appreciated.  (As the comment
on the related pair A000945 & A000946 says "The computational problem inherent
in continuing the sequence further is the enormous size of the numbers that
must be factored.")  Thanks!

%I A084599
%S A084599 2 3 5 29 11 7 13 37 32222189 131 136013303998782209 31 197 19
%N A084599 a(1) = 2, a(2)=3, a(n+1) is largest prime factor of Product_{k=1..n}
a(k) - 1
%C A084599 Like the Euclid-Mullin sequence A000946, but subtracting rather
than adding 1 to the product.  When does this sequence diverge from A084598?
%e A084599 a(4)=29 since 2*3*5=30 and 29 is the smallest prime factor of
%Y A084599 Cf. A000946, A084598
%O A084599 1
%K A084599 ,more,nonn,
%A A084599 Marc LeBrun (mlb at, May 31 2003

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