Re: [math-fun] sums of three triangular numbers etc

On Aug 28, 2015, at 12:18 PM, Neil Sloane <njasloane@gmail.com> wrote:

My question is, what is the least dense sequence S that works? One might think that one only needs O(N^(1/3)) terms below N to get S+S+S = Z+ This seems pretty efficient (in base 3):

1 2 10 20 100 200 1000 1001 1002 2000 2001 2002 10000 10010 10020 20000 20010 20020 100000 100100 100200 200000 200100 200200 1000000 1000001 1000002 1001000 1001001 1001002 1002000 1002001 1002002 2000000 2000001 2000002 2001000 2001001 2001002 2002000 2002001 2002002 etc. -Veit