[seqfan] Will this pattern continue?

[Ali Sada]

Hi everyone,

We take the twin primes and put them in pairs
(3,5), (5,7), (11,13), (17,19), etc.

We find the least triangular number that is a multiple of both primes in each pair 

15, 105, 2145, 11628, 94395, 370230, 1565565, 3265290, 13263825, 16689753, 44674878, 62434725, 129757995, 168095280, 190173753, 334822503, 411256860, 659371455, 784892010, 1176876870, 1822721253  
(This is the best my computer and my computing skills can reach)

Now, we divide each of these numbers by its two primes and we get 

1, 3, 15, 36, 105, 210, 435, 630, 1275, 1431, 2346, 2775, 4005, 4560, 4851, 6441, 7140, 9045, 9870, 12090, 15051

So far, these are all triangular numbers. Will this pattern continue? 

These triangular numbers correspond to:
1, 2, 5, 8, 14, 20, 29, 35, 50, 53, 68, 74, 89, 95, 98, 113, 119, 134, 140, 155, 173 (I would like to add this sequence to the OEIS if the editors think it's suitable.) 

If we exclude the first term, the differences between the terms are 
3, 3, 6, 6, 9, 6, 15, 3, 15, 6, 15, 6, 3, 15, 6, 15, 6, 15, 18

These are multiples of 3. Which is another potential pattern. 

We divide them by three and we get this "bareboned" sequence
1, 1, 2, 2, 3, 2, 5, 1, 5, 2, 5, 2, 1, 5, 2, 5, 2, 5, 6 ( I would love to add this sequence too if possible)

I appreciate your feedback in advance. 

Best,

Ali