A138798 Values of j corresponding to least possible k>0 with T(k)-T(j)=n, where T(i)>0 are the triangular numbers A000217.

1, 2, 3, 1, 5, 2, 7, 1, 9, 4, 2, 5, 1, 3, 15, 7, 2, 8, 1, 5, 3, 10, 6, 2, 4, 1, 27, 13, 3, 14, 31, 2, 6, 1, 10, 17, 7, 3, 5, 19, 2, 20, 1, 4, 9, 22, 14, 3, 7, 5, 2, 25, 1, 8, 4, 6, 12, 28, 3, 29, 13, 2, 63, 1, 14, 32, 4, 8, 6, 34, 3, 35, 16, 2, 5, 1, 17, 38, 13, 4, 18, 40, 6, 3, 19, 11, 2, 43, 1

Offset: 2

Author

Peter Pein (petsie(AT)dordos.net), Mar 30 2008

Keywords

• nonn

Comments

For k see A138796, for T(k) see A138797 and for T(j) see A138799.

The number of ways n can be written as difference of two triangular numbers is sequence A136107

Examples

			a(30)=3 because 30 = T(30)-T(29)=T(11)-T(8)=T(9)-T(5)=T(8)-T(3) and 3 is the least index of the subtrahends.
		

Crossrefs

Cf. A000217, A109814, A118235, A136107, A138796, A138797, A138799.

Programs

Mathematica

T=#(#+1)/2&;Sort[{k,j}/.{ToRules[Reduce[{T[k]-T[j]\[Equal]#,0