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

0,2

Comments

The first occurrence of n in A136107

Links

Table of n, a(n) for n=0..37.

Example

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.

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

Crossrefs

Cf. A136107.

Sequence in context: A344394 A243559 A334077 * A026297 A109742 A072979

Adjacent sequences: A136105 A136106 A136107 * A136109 A136110 A136111

Keyword

nonn

Author

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

Extensions

6 new terms from Donovan Johnson, Jan 21 2009

a(37) from Max Alekseyev, May 13 2009

Status

approved