A023365 a(n) = 2^(3^(n-1)).

2, 8, 512, 134217728, 2417851639229258349412352, 14134776518227074636666380005943348126619871175004951664972849610340958208

Offset

1,1

Comments

a(n+1) = a(n) converted to base 8 from base 2 (written in base 10).

Number of disjunctive-normal forms of n-1 variables (either with x, or x-negated or without x). - Labos Elemer, Jul 24 2003

a(n)*Psi(3^n,x), with the (monic) minimal polynomial Psi(3^n,x) of cos(2*Pi/3^n), becomes an integer polynomial with coefficient 1 of x^0.

E.g., 8*Psi(9,x)=8*(x^3 - (3/4)*x + 1/8) = 8*x^3 - 6*x + 1.

See A181875/A181876, A181877 and the W. Lang link under A181875. - Wolfdieter Lang, Feb 24 2011

The next term (a(7)) has 220 digits. - Harvey P. Dale, Aug 10 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..8

W. van der Aalst, J. Buijs and B. van Dongen, Towards Improving the Representational Bias of Process Mining, 2012. - From N. J. A. Sloane, Feb 03 2013

Formula

a(n) = a(n-1)^3.

Mathematica

NestList[#^3&, 2, 6] (* Harvey P. Dale, Aug 10 2014 *)

Prog

(Magma) [Floor(2^(3^(n-1))): n in [1..10]]; // Vincenzo Librandi, Aug 11 2014

Crossrefs

a(n) = A000079(A000244(n-1)).

Sequence in context: A033542 A098870 A221065 * A262826 A013554 A175923

Adjacent sequences: A023362 A023363 A023364 * A023366 A023367 A023368

Keyword

nonn

Author

David W. Wilson

Status

approved