A371636 For any number k >= 0, let T_k be the triangle with values in {-1, 0, +1} whose base corresponds to the balanced ternary expansion of k (without leading zeros) and other values, say t above u and v, satisfy t+u+v = 0 mod 3; this sequence lists the numbers k such that T_k has 3-fold rotational symmetry.

0, 1, 4, 13, 19, 25, 40, 103, 112, 121, 154, 214, 364, 442, 505, 595, 673, 763, 826, 913, 1003, 1093, 1144, 1369, 1621, 1915, 2167, 2392, 2776, 3028, 3280, 3628, 4420, 4996, 5668, 6244, 7036, 8203, 9022, 9841, 10459, 10594, 11782, 12304, 13411, 13627, 14419

Offset: 1

Author

Rémy Sigrist, Mar 30 2024

Keywords

• nonn
• base

Comments

This sequence is a variant of A334556 and A361818.

This sequence is infinite as it contains A003462.

Empirically, for any w > 0, there are A127975(w-1) terms with w balanced ternary digits (ignoring leading zeros).

If k is a term then A338246(k) is also a term.

Examples

			The balanced ternary expansion of 595 is "1T11001" (where T denotes -1), and the corresponding triangle T_595 is as follows:
           1
          T 0
         1 0 0
        1 1 T 1
       0 T 0 1 1
      0 0 1 T 0 T
     1 T 1 1 0 0 1
As this triangle has 3-fold rotational symmetry, 595 belongs to the sequence.
		

Links

• Rémy Sigrist, Triangles illustrating initial terms (blue, gray and red respectively denote -1's, 0's and 1's)
• Rémy Sigrist, PARI program
• Index entries for sequences related to XOR-triangles

Crossrefs

Cf. A003462, A127975, A334556, A338246, A361818, A371635.

Programs

PARI

\\ See Links section.