login
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.
1
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.
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 26 2023
STATUS
approved