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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.
2
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
1,3
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.
LINKS
Rémy Sigrist, Triangles illustrating initial terms (blue, gray and red respectively denote -1's, 0's and 1's)
Rémy Sigrist, PARI program
EXAMPLE
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.
PROG
(PARI) \\ See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 30 2024
STATUS
approved