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%I #26 Dec 06 2015 15:12:49
%S 3,2,7,41,1723,5,14835031,220078129935929,241,23,79,101,23291,11,223,
%T 122386298896281959929015788890561251765109069,38803,17,8209,59,199,
%U 3340389589,11527,13,47939,1163,599,27198087874669514440553,181936481,31,383,9623,739,33287,1061,6493520653,587,709,6548057,1823,361789,20183
%N a(1)=3; for n>1, if n is odd a(n) = spf(Product_{k=1..n-1}(a(k))+1) else a(n) = spf(Product_{k=1..n-1}(a(k))-1), where spf is "smallest prime factor".
%t a[1] = 3; a[n_] := a[n] = FactorInteger[ Product[a[k], {k, n - 1}] + If[OddQ@ n, 1, -1]][[1, 1]]; Array[a, {16}] (* _Michael De Vlieger_, Nov 30 2015 *)
%o (PARI) spf(n)=my(f=factor(n)[1, 1]); f
%o first(m)=my(v=vector(m)); v[1]=3; for(i=2, m,;v[i]=spf((-1)^(i+1)+prod(j=1, i-1, v[j]))); v
%Y Cf. A000945, A005265.
%K nonn
%O 1,1
%A _Anders Hellström_, Nov 30 2015
%E a(20)-a(42) from _Hans Havermann_, Dec 06 2015