A165428 a(1) = 1, a(2) = 10; thereafter a(n) = Product_{1 <= i <= n-1} a(i).

1, 10, 10, 100, 10000, 100000000, 10000000000000000, 100000000000000000000000000000000, 10000000000000000000000000000000000000000000000000000000000000000

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..12

Formula

a(n) = 10^(2^(n-3)) = A011557(2^(n-3)) = 10^A000079(n-3).

a(1) = 1, a(2) = 10, a(3) = 10, and for n > 3 a(n) = (a(n-1))^2.

From Amiram Eldar, Nov 30 2025: (Start)

Sum_{n>=1} 1/a(n) = 11/10 + A036987 (interpreted as a constant).

Product_{n>=1} (1 + 1/a(n)) = 22/9. (End)

Mathematica

a[1] = 1; a[2] = 10; a[n_] := Times @@ Array[a, n - 1]; Array[a, 9] (* Robert G. Wilson v, Oct 13 2009 *)
Join[{1, 10}, NestList[#^2&, 10, 10]] (* Harvey P. Dale, Nov 30 2021 *)

Prog

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

Crossrefs

Cf. A000079, A011557, A036987.

Sequence in context: A285613 A288301 A287602 * A288495 A288765 A287743

Adjacent sequences: A165425 A165426 A165427 * A165429 A165430 A165431

Keyword

nonn

Author

Jaroslav Krizek, Sep 17 2009

Extensions

Name changed, formula edited by Robert G. Wilson v, Oct 13 2009

Edited by N. J. A. Sloane, Oct 15 2009

Status

approved