A165421 a(1) = 1, a(2) = 3, a(n) = product of the previous terms for n >= 3.

1, 3, 3, 9, 81, 6561, 43046721, 1853020188851841, 3433683820292512484657849089281, 11790184577738583171520872861412518665678211592275841109096961

Offset: 1

Author

Jaroslav Krizek, Sep 17 2009

Keywords

• nonn

Comments

Essentially a duplicate of A011764. - N. J. A. Sloane, Oct 06 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..14

Programs

Mathematica

a[1]:= 1; a[2]:= 3; a[n_]:= Product[a[j], {j,1,n-1}]; Table[a[n], {n, 1, 12}] (* G. C. Greubel, Oct 19 2018 *)
nxt[{prd_,a_}]:=Module[{c=prd*a},{c,prd*a}]; Join[{1,3},Rest[ NestList[ nxt,{1,3},10][[All,1]]]] (* Harvey P. Dale, Jan 31 2022 *)

PARI

{a(n) = if(n==1, 1, if(n==2, 3, prod(j=1,n-1, a(j))))};
for(n=1,10, print1(a(n), ", ")) \\ G. C. Greubel, Oct 19 2018

Formula

a(1) = 1, a(2) = 3, a(n) = Product_{i=1..n-1} a(i), n >= 3.

a(1) = 1, a(2) = 3, a(n) = A000244(2^(n-3)) = A011764(n-3) = 3^(2^(n-3)), n >= 3.

a(1) = 1, a(2) = 3, a(3) = 3, a(n) = (a(n-1))^2, n >= 4.