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).
# Python 2.7.7 Code # Jonathan Frech 13th of July, 2016 # edited 15th of July, 2016