On Monday 05 December 2005 09:46, Eric Angelini wrote:

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 ?

If you really mean "digits", then of course it does, because no term can be larger than 90, and so there are only 90^10 possibilities for the last 10 numbers, and the last 10 numbers determine the last 10 digits, so everything repeats with period at most 90^10. If you mean "numbers", then of course it doesn't, because the sequence is strictly increasing (after the 1,1 terms). Am I misunderstanding the question? -- g