- #1
honestrosewater
Gold Member
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I think this will be my new mantra ;) but it is actually related to the question.
I want to define the sequence (s_n) where n is natural and whose nth term, t_n, is the sum of the digits of n.
I want to do this without using Gauss's modular arithmetic. This may be one of those 'easier said than done' problems. But I find it hard to believe that everyone (ex. Euler) was completely stumped by it before Gauss came along.
At the moment, I'm thinking that factorials may play a part. Besides the more obvious reasons why, the fact that 0! = 1 might help with the equivalence between 0 and 9 that must eventually be handled.
Anyway, just thought I'd see if anyone has anything to add.
Happy thoughts
Rachel
I want to define the sequence (s_n) where n is natural and whose nth term, t_n, is the sum of the digits of n.
I want to do this without using Gauss's modular arithmetic. This may be one of those 'easier said than done' problems. But I find it hard to believe that everyone (ex. Euler) was completely stumped by it before Gauss came along.
At the moment, I'm thinking that factorials may play a part. Besides the more obvious reasons why, the fact that 0! = 1 might help with the equivalence between 0 and 9 that must eventually be handled.
Anyway, just thought I'd see if anyone has anything to add.
Happy thoughts
Rachel