Does this list end with 5 numbers, is there a proof that it couldn't continue indefinitely.
According to this link, there are only four (I don't think repeating 1 should count toward this number). I have no time to think about why though-either that 1989 reference was simply the most convenient or well-known, or it was the first appearance of the proof, in which case it might be a pretty hard proof. ``
In 1989, L. Ming proved the only Fibonacci numbers which are triangular are 1, 3, 21, and 55. Please refer to Ming, L. "On Triangular Fibonacci Numbers." Fib. Quart. 27, 98-108, 1989.
The Fibonacci Sequence is the series of numbers:
The next number is found by adding up the two numbers before it.
The general formula is `T_n=T_(n-1)+T_(n-2)`
On the other hand, the Triangular Number Sequence is:
Five Fibonacci numbers that are also triangular numbers are 1,1,3,21,55.