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

0,3

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

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

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 *)

Crossrefs

Complement of A134026.

Sequence in context: A246261 A220695 A079258 * A109406 A280632 A178462

Adjacent sequences: A134022 A134023 A134024 * A134026 A134027 A134028

Keyword

nonn,base

Author

Reinhard Zumkeller, Oct 19 2007

Status

approved