Intended for: December 1, 2011
Timetable
 First draft entered by Alonso del Arte on August 28, 2011 ✓
 Draft reviewed by Daniel Forgues on December 1, 2011 ✓
 Draft to be approved by November 1, 2011
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A188892: Numbers
such that there is no triangular
gonal number greater than
1.

{ 11, 18, 38, 102, 198, 326, 486, ... }
The
triangular numbers are essentially the building blocks of the other
figurate numbers. Therefore it is rather surprising that there can be sequences of
gonal numbers that don’t overlap with the sequence of triangular numbers at all (other than
0 and
1).
T. D. Noe has demonstrated that the equation
x 2 + x = (n − 2) y 2 − (n − 4) y 
has no integer solutions
, as conversion to a
generalized Pell equation shows that if
, then the first equation has only a finite number of solutions. From there one can pinpoint those values of
that produce no integer solutions greater than
1.