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%I #17 Apr 25 2016 11:45:33
%S 2,3,5,11,41,7,23,17,19,13,37,53,73,151,29,43,31,59,71,47,79,61,107,
%T 83,103,163,109,89,101,113,67,97,137,131,139,127,229,149,173,227,179,
%U 239,181,191,193,167,197,241,277,157,233,211,397,257,271,283,251,281,313,269,347,349,317,263,379,223,367,199,353,401,421,463,293,337,383,389,331,431,359,443
%N a(n+1) is the smallest prime factor of any (Product_{k=1..j} a(k)) + (Product_{k=j+1..n} a(k)) for j=0..n.
%e For n=4, a = <2,3,5>, yielding sums <1+2*3*5, 2+3*5, 2*3+5, 2*3*5+1> = <31,17,11,31>, with least prime factor a(4)=11.
%o (PARI) prodsum(ls) = local(left=1, right=prod(x=1,#ls,ls[x]), o=vector(#ls)); for(x=1,#ls,left*=ls[x];right/=ls[x];o[x]=left+right);o
%o newlpf(v) = local(l=0, fs); for(x=1,#v,fs=factor(v[x],if(l>500000,0,l));if(!l||fs[1,1]<l,l=fs[1,1]));l
%o s=[2]; while(#s<80,s=concat(s,[newlpf(prodsum(s))]))
%Y A modification of A000945, the Euclid-Mullin sequence, which looks only at factors from the j=n term.
%K nonn,easy
%O 1,1
%A _Phil Carmody_, Feb 23 2013
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