login
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.
3
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
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]
KEYWORD
nonn
AUTHOR
Peter Pein (petsie(AT)dordos.net), Mar 30 2008
STATUS
approved