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

2,2

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

Links

Table of n, a(n) for n=2..90.

Example

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.

Mathematica

T=#(#+1)/2&; Sort[{k, j}/.{ToRules[Reduce[{T[k]-T[j]\[Equal]#, 0<j<k}, {j, k}, Integers]]}][[1, 2]]&/@Range[2, 100]

Crossrefs

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

Sequence in context: A308707 A158584 A086112 * A277708 A360496 A356473

Adjacent sequences: A138795 A138796 A138797 * A138799 A138800 A138801

Keyword

nonn

Author

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

Status

approved