A138799 Values of T(j) corresponding to least possible T(k) with T(k)-T(j)=n, where T(i)>0 are the triangular numbers A000217.

1, 3, 6, 1, 15, 3, 28, 1, 45, 10, 3, 15, 1, 6, 120, 28, 3, 36, 1, 15, 6, 55, 21, 3, 10, 1, 378, 91, 6, 105, 496, 3, 21, 1, 55, 153, 28, 6, 15, 190, 3, 210, 1, 10, 45, 253, 105, 6, 28, 15, 3, 325, 1, 36, 10, 21, 78, 406, 6, 435, 91, 3, 2016, 1, 105, 528, 10, 36, 21, 595, 6, 630

Offset

2,2

Comments

For k see A138796, for T(k) see A138797 and for j see A138798.

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..73.

Example

a(30)=6 because 30 = T(30)-T(29)=T(11)-T(8)=T(9)-T(5)=T(8)-T(3) and T(3)=6 is the least minuend.

Mathematica

T=#(#+1)/2&; T[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, A138798.

Sequence in context: A100960 A130852 A228335 * A321480 A334879 A108441

Adjacent sequences: A138796 A138797 A138798 * A138800 A138801 A138802

Keyword

nonn

Author

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

Status

approved