%I #4 Dec 23 2018 03:45:56

%S 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,

%T 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,

%U 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

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

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

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

%e 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.

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

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

%K nonn

%O 2,2

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