A259255 With a(1) = 1, a(n) is the smallest number not already in the sequence such that -1 + Product_{i=1..n} a(i) is a square.
1, 2, 5, 17, 13, 97, 3077, 155333, 147223992353, 182758163483477540989, 634072602906397751091977058984828897557
Offset: 1
Programs
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PARI
v=[1];n=1;while(n<10^6,s=-1+n*prod(i=1,#v,v[i]);if(issquare(s)&&! vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v
Extensions
a(9)-a(11) from Giovanni Resta, Jun 22 2015