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.

1, 3, 6, 7, 18, 36, 148, 5625, 351225, 5350321, 151875880681, 247160867363588025, 126888381222131340236953809, 592938336545755964751256254689753896569

Offset: 1

Author

Derek Orr, Jun 22 2015

Keywords

• nonn
• easy

Links

• Giovanni Resta, Table of n, a(n) for n = 1..22 (terms < 10^1000)

Crossrefs

Cf. A259255, A094353, A067836.

Programs

Mathematica

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 *)

PARI

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

Extensions

a(11)-a(14) from Giovanni Resta, Jun 22 2015