A055156 Powers of 3 which are not powers of 3^3.

3, 9, 81, 243, 2187, 6561, 59049, 177147, 1594323, 4782969, 43046721, 129140163, 1162261467, 3486784401, 31381059609, 94143178827, 847288609443, 2541865828329, 22876792454961, 68630377364883, 617673396283947, 1853020188851841, 16677181699666569, 50031545098999707

Offset

0,1

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (0,27).

Formula

a(n) = a(n-1)*a(n-2)/a(n-3) = 27*a(n-2) = 3^A001651(n).

a(2*n) = 3^(3*n+1), a(2*n+1) = 3^(3*n+2).

From Amiram Eldar, Feb 20 2026: (Start)

Sum_{n>=0} 1/a(n) = 6/13.

Sum_{n>=0} (-1)^n/a(n) = 3/13. (End)

G.f.: -3*(3*x + 1)/(27*x^2 - 1). - Elmo R. Oliveira, Apr 01 2026

Mathematica

With[{nn=40}, Complement[3^Range[nn], 27^Range[Floor[nn/3]]]] (* or *) LinearRecurrence[{0, 27}, {3, 9}, 40] (* Harvey P. Dale, Jul 17 2012 *)

Crossrefs

Cf. A001651, A013732, A013733.

Consists of numbers in A000244 which are not in A009971.

Cf. A004171 (powers of 2 which are not powers of 2^2).

Sequence in context: A124049 A067623 A171557 * A047912 A078684 A121858

Adjacent sequences: A055153 A055154 A055155 * A055157 A055158 A055159

Keyword

nonn,easy

Author

Henry Bottomley, Jun 20 2000

Status

approved