A361827 For any number k >= 0, let T_k be the triangle whose base corresponds to the ternary expansion of k (without leading zeros) and other values, say t above u and v, satisfy t = (-u-v) mod 3; this sequence lists the numbers k such that the configurations of 0's, 1's and 2's in T_k are the same up to rotation.

3, 5, 6, 7, 11, 15, 19, 21, 84, 93, 102, 140, 149, 158, 168, 177, 186, 196, 205, 214, 308, 318, 351, 377, 410, 420, 528, 532, 574, 588, 702, 715, 2271, 2396, 2523, 2621, 2775, 2873, 2933, 3150, 3185, 3375, 3410, 3627, 3687, 3785, 3939, 4037, 4164, 4289, 4519

Offset: 1

Author

Rémy Sigrist, Mar 26 2023

Keywords

• nonn
• base

Comments

This sequence is a variant of A361818.

If k belongs to the sequence, then A004488(k) belongs to the sequence.

The ternary lengths of terms belong to A007494 (as the number of values in triangles must be divisible by 3).

This sequence is infinite as it contains the numbers whose ternary digits match the regular expression "(210)+".

Empirically, there are 4*3^floor((w-1)/2) terms with w ternary digits.

No term belongs to A297250.

Examples

			The ternary expansion of 149 is "12112", and the corresponding triangle is:
            0
           1 2
          0 2 2
         0 0 1 0
        1 2 1 1 2
The configurations of 0's, 1's and 2's are the same up to rotation, so 149 belongs to this sequence:
            0            .            .
           . .          1 .          . 2
          0 . .        . . .        . 2 2
         0 0 . 0      . . 1 .      . . . .
        . . . . .    1 . 1 1 .    . 2 . . 2
		

Links

• Rémy Sigrist, Triangles illustrating initial terms
• Rémy Sigrist, PARI program
• Index entries for sequences related to XOR-triangles

Crossrefs

Cf. A004488, A007494, A297250, A361818.

Programs

PARI

See Links section.