OFFSET
1,3
COMMENTS
We can devise a similar sequence for any fixed base b >= 2; the present sequence corresponds to b = 3, and A334556 corresponds to b = 2.
This sequence is infinite as it contains A048328.
Empirically, there are 2*3^floor((w-1)/3) positive terms with w ternary digits.
For any k, if t appears above u and v in T_k, then t + u + v = 0 (mod 3) and #{t, u, v} = 1 or 3 (the three values are either equal or all distinct); each value is uniquely determined by the two others in the same way: t = (-u-v) mod 3, u = (-t-v) mod 3, v = (-t-u) mod 3; this means that we can reconstruct T_k from any of its three sides.
If some row of T_k, say r, has w values and corresponds to the ternary expansion of m, then the row above r corresponds to the w-1 rightmost digits of the ternary expansion of A060587(m).
All positive terms belong to A297250 (their most significant digit equals their least significant digit in base 3).
LINKS
EXAMPLE
The ternary expansion of 304 is "102021", and the corresponding triangle is:
1
0 2
2 1 0
0 1 1 2
2 1 1 1 0
1 0 2 0 2 1
As this triangle has 3-fold rotational symmetry, 304 belongs to the sequence.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 25 2023
STATUS
approved