A134025 Numbers for which the balanced ternary representation is the same length as the ternary representation.

0, 1, 3, 4, 9, 10, 11, 12, 13, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121

Offset: 0

Author

Reinhard Zumkeller, Oct 19 2007

Keywords

• nonn
• base

Comments

A003462 is a subsequence; A171960(a(n)) >= a(n). - Reinhard Zumkeller, Jan 20 2010

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Complement of A134026.

Programs

Maple

0,seq($3^(d-1)..floor(3^d/2), d=0..5); # Robert Israel, Dec 14 2015

Mathematica

f[n_, m_, k_] := If[n == 0, k, If[k < (3^(m + 1) - 1)/2, f[n - 1, m, k + 1], f[n - 1, m + 1, 3^(m + 1)]]]; Table[f[n, 0, 0], {n, 0, 63}] (* L. Edson Jeffery, Dec 10 2015 *)

Formula

a(n) = f(n,0,0) with f(n,m,k) = if n=0 then k else if k<(3^(m+1)-1)/2 then f(n-1,m,k+1) else f(n-1,m+1,3^(m+1)).

A134021(a(n)) = A081604(a(n)).

G.f.: x/(1-x)^2 + (1-x)^(-1)*Sum_{j>=1} ((3^j-1)/2) * x^(3/4 + 3^j/2 + j/2). - Robert Israel, Dec 14 2015