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.
The following is in the <noinclude> ... </noinclude> section.
For more details about today's Sequence of the Day, see {{Sequence of the Day for December 1}}.
Guidelines for selecting the Sequence of the Day
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