Diophantine sequence

[Ed Pegg]

2^n - 2 = 7(x^2 - x) + (y^2 - y)

Euler proved that the above diophantine equation has a unique solution for
any n.  (Engel, Problem-Solving Strategies)  He never published his result
or proof.

This leads to an odd set of sequences:
{1, 2, 3, 1, 6, 5, 7, 16, 3, 29, 34, 24, 91, 44, 138, 225, 51, 500, 399,
601, 1398}
{1, 1, 1, 2, 1, 3, 4, 2, 9, 6, 12, 23, 1, 46, 45, 47, 136, 43, 229, 314,
144}

But perhaps this is too obscure.

--Ed Pegg Jr.