A136108 The least number k such that there are n different representations of k as the difference of two positive triangular numbers.

1, 2, 5, 9, 27, 45, 63, 105, 135, 225, 405, 630, 315, 531441, 3645, 1485, 945, 4851, 1575, 13041, 2835, 18225, 295245, 4095, 3465, 50625, 2657205, 11025, 25515, 52650, 14175, 17955, 10395, 1476225, 215233605, 97020, 17325, 150094635296999121

Offset: 0

Author

John W. Layman and Robert G. Wilson v, Dec 12 2007

Keywords

• nonn

Comments

The first occurrence of n in A136107

Examples

			a(0)=1 because there are no two positive triangular numbers whose difference is 1,
a(1)=2 because 3-1 = 2,
a(2)=5 because 6-1 = 15-10 = 5,
a(3)=9 because 10-1 = 15-6 = 45-36 = 9, etc.
		

Crossrefs

Cf. A136107.

Programs

Mathematica

f[n_] := f[n] = Block[{c = 0, k = 1}, While[k < n, If[IntegerQ[Sqrt[8 n + 4 k (k + 1) + 1]], c++ ]; k++ ]; c]; Table[ Position[ Table[ f@i, {i, 54000}], n, 1, 1], {n, 0, 30}] // Flatten

Extensions

6 new terms from Donovan Johnson, Jan 21 2009

a(37) from Max Alekseyev, May 13 2009