[math-fun] Sum of last ten digits

Start with 0 0 0 0 0 0 0 0 0 1 Next term is the sum of the last 10 digits: 0 0 0 0 0 0 0 0 0 1 1 Next term is the sum of the last 10 digits: 0 0 0 0 0 0 0 0 0 1 1 2 Next term is the sum of the last 10 digits: 0 0 0 0 0 0 0 0 0 1 1 2 4 etc. Does this sequence enter in a loop ? Best,