Triangle Numbers & Numbers Written in Base of Triangle Numbers.

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I'm failing to see the relation between triangle numbers and numbers written in base of triangle numbers.

 

Can somebody explain this to me?

[John]

Is this a homework question, or is it something you need to know to answer a homework question? It's hard to give hints here without just giving away the answer immediately, but I can try:

If we write a number in base n, then we're using a system of n digits (usually from 0 to n - 1), with each position representing a power of n. For instance, in our usual base 10, we write the number 243 to represent 2 * 10² + 4 * 10¹ + 3 * 10⁰.

 

So you have this list of numbers written in "base of triangular numbers." Comparing the lists and in light of what we mean by numbers in base n, you might notice the pattern.

Edited April 7, 2014 by John