A085239 Sort the numbers 2^i and 3^j. Then a(n) is the base of the n-th term. Set a(1)=1.

1, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2

Offset: 1

Author

Reinhard Zumkeller, Jun 22 2003

Keywords

• nonn

Comments

The density of 2's in this sequence is log(3)/log(6). The density of 3's in this sequence is log(2)/log(6). - Jennifer Buckley, Apr 24 2024

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..500 from T. D. Noe)

Crossrefs

Cf. A000079, A000244.

Cf. A006899, A085238.

Cf. A152683, A152935.

Programs

Haskell

a085239 1 = 1
a085239 n = a006899 n `mod` 2 + 2  -- Reinhard Zumkeller, Oct 09 2013

Mathematica

m = 40;
Join[{1}, If[Total[IntegerDigits[#, 2]] == 1, 2, 3]& /@ Union[3^Range[m], 2^Range[Length[IntegerDigits[3^m, 2]] - 1]]] (* Jean-François Alcover, Oct 07 2021 *)

PARI

upto(L) = my(v2=2, v3=1, r=List(1)); while(v3Ruud H.G. van Tol, May 10 2024

Python

from sympy import integer_log
def A085239(n): return 1 if n==1 else 2 if 6**integer_log(m:=3**(n-1),6)[0]<<1Chai Wah Wu, Feb 04 2025

Formula

A006899(n) = a(n)^A085238(n).

For n > 1: a(n) = 2 + A006899(n) mod 2. - Reinhard Zumkeller, Oct 09 2013