Triangular Squares (#133)
Jonathan Frech
In a recent video, Matt Parker showed a triangular number that also is a square number, 6, and asked if there were more.
A triangular number has the form — shown by Euler — and a square number has the form
.
Triangular squares are those numbers for which with
.
Examples are (sequence A001109 in OEIS).
To check if triangular numbers are square numbers is easy (code listed below), but a mathematical function would be nicer.
The first thing I tried was to define the triangular number’s square root as a whole number, . This function does not return the square numbers that are triangular but the triangular numbers that are square.
The resulting sequence is (sequence A001108 in OEIS).
Source code: triangular-squares.py