Triangular Numbers and a Sequence

  1. Fill a 4x3 grid with individual digits, such that the three 4-digit numbers and the four 3-digit numbers are all triangular.
  2. What are the last two numbers in this sequence?
    10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, 31, 100, 121, ..?.., ..?..

Source: 1. Reader Hareendra Yalamanchili (later found at www.mathpuzzle.com for April 22.) 2. Reader Peter Bentley.

Solutions were received from Andrew Ofiesh, Dan Ghinea, Claudio Baiocchi, Sudipta Das, Samantha Levin, Stephane Higueret, and Denis Borris. Solutions are:
  1. The answer is unique. (Here's the answer from www.mathpuzzle.com.) 
    3321
5050
1035
  2. From the On-line Encyclopedia of Integer Sequences: 
    ID Number: A008713
Sequence:  10,11,12,13,14,15,16,17,20,22,24,31,100,121,10000,
           1111111111111111
Name:      16 in base 16-n.
Example:   16 is 121 in base 3, so a(13)=121.
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