I'm trying to invent a new type of number who's digits are composed of hybrid 'Discrete Triangular Number Base' numbers (Which have two components; one in 'Discrete Triangular Number Base X and Base Y' and the other in Base 1)
Some examples are:
Base X = 4 and Base Y = 2
Generating Hybrid Triangle Base Numbers [Triangle Base 4] and [Base 2] in [Base 1] numbers 0 to 10
NUMBER [4 3 2 1] [4 3 2 1] TRIANGLE BASE NUMBER
; [1 1 1 1] [1 1 1 1]
0 [0 0 0 0] [0 0 0 0] 0:0
1 [0 0 0 0] [0 0 0 1] 0:1
2 [0 0 0 0] [0 0 1 1] 0:2
3 [0 0 0 0] [0 1 1 1] 0:3
4 [0 0 0 0] [1 0 0 0] 4:0
5 [0 0 0 0] [1 0 0 1] 4:1
6 [0 0 0 0] [1 0 1 1] 4:2
7 [0 0 0 0] [1 1 0 0] 7:0
8 [0 0 0 0] [1 1 0 1] 7:1
9 [0 0 0 0] [1 1 1 0] 9:0
10 [0 0 0 1] [0 0 0 0] 0:1|0:0
FINISHED GENERATING NUMBERS
Base X = 4 and Base Y = 3
Generating Hybrid Triangle Base Numbers [Triangle Base 4] and [Base 3] in [Base 1] numbers 0 to 20
NUMBER [4 3 2 1] [4 3 2 1] TRIANGLE BASE NUMBER
; [1 1 1 1] [1 1 1 1]
0 [0 0 0 0] [0 0 0 0] 0:0
1 [0 0 0 0] [0 0 0 1] 0:1
2 [0 0 0 0] [0 0 0 2] 0:2
3 [0 0 0 0] [0 0 1 2] 0:3
4 [0 0 0 0] [0 0 2 2] 0:4
5 [0 0 0 0] [0 1 2 2] 0:5
6 [0 0 0 0] [0 2 2 2] 0:6
7 [0 0 0 0] [1 2 2 2] 0:7
8 [0 0 0 0] [2 0 0 0] 8:0
9 [0 0 0 0] [2 0 0 1] 8:1
10 [0 0 0 0] [2 0 0 2] 8:2
11 [0 0 0 0] [2 0 1 2] 8:3
12 [0 0 0 0] [2 0 2 2] 8:4
13 [0 0 0 0] [2 1 2 2] 8:5
14 [0 0 0 0] [2 2 0 0] 14:0
15 [0 0 0 0] [2 2 0 1] 14:1
16 [0 0 0 0] [2 2 0 2] 14:2
17 [0 0 0 0] [2 2 1 2] 14:3
18 [0 0 0 0] [2 2 2 0] 18:0
19 [0 0 0 0] [2 2 2 1] 18:1
20 [0 0 0 1] [0 0 0 0] 0:1|0:0
FINISHED GENERATING NUMBERS
My current progress is trying to figure out how the second component can be represented in Base 2