A094354
Squares arising as a partial product in A094353 + 1.
Original entry on oeis.org
4, 4, 16, 121, 841, 1681, 28561, 1256641, 66601921, 67334541121, 489048684783785281, 13573985927350210047691125121, 145428587993834208572289541475484929400094613761
Offset: 1
3+1= 4, 3*1*5 +1 = 16, 3*1*5*8 +1 = 121 etc. are squares.
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.
Original entry on oeis.org
1, 2, 5, 17, 13, 97, 3077, 155333, 147223992353, 182758163483477540989, 634072602906397751091977058984828897557
Offset: 1
-
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
A259256
With a(1) = 1, a(n) is the smallest number not already in the sequence such that a(n) + Product_{i=1..n-1} a(i) is a square.
Original entry on oeis.org
1, 3, 6, 7, 18, 36, 148, 5625, 351225, 5350321, 151875880681, 247160867363588025, 126888381222131340236953809, 592938336545755964751256254689753896569
Offset: 1
-
L = {1}; While[Length[L] < 22, p = Times @@ L; q = Ceiling[Sqrt[p + 1]]; While[ MemberQ[L, q^2 - p], q++]; AppendTo[L, q^2 - p]]; L (* Giovanni Resta, Jun 22 2015 *)
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v=[1];n=1;while(n<10^7,s=n+prod(i=1,#v,v[i]);if(issquare(s)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v
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