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

1,1

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.

Links

Table of n, a(n) for n=1..51.

Rémy Sigrist, Triangles illustrating initial terms

Rémy Sigrist, PARI program

Index entries for sequences related to XOR-triangles

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A004488, A007494, A297250, A361818.

Sequence in context: A301975 A015814 A227026 * A053272 A326929 A138927

Adjacent sequences: A361824 A361825 A361826 * A361828 A361829 A361830

Keyword

nonn,base

Author

Rémy Sigrist, Mar 26 2023

Status

approved