How would you describe the sequence of numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, ...?

**Nota Bene**: You're not allowed use a computer program or code to describe it.

How would you describe the sequence of numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, ...?

**Nota Bene**: You're not allowed use a computer program or code to describe it.

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TopNewestHint: Apply the general formula for \(C_{10} \) for Champernowne constant. Then 10 raise to the power of respective digits, then mod 10 answer. The full working is very long and ugly. – Pi Han Goh · 1 year, 1 month agoLog in to reply

\[T_n = \lfloor 10^{n} \times C_{10} \rfloor \pmod{10}\] – Sharky Kesa · 1 year, 1 month ago

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\[\large T_k = \left \lfloor 10^k \times \displaystyle \sum_{m=0}^{\infty} \sum_{n=10^{m-1}}^{10^m - 1} \dfrac {n}{10^{m(n - 10^{m - 1} + 1) + 9 \sum_{l=1}^{m-1} 10^{l-1} l}} \right \rfloor \pmod{10}\] – Sharky Kesa · 1 year, 1 month ago

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– Sharky Kesa · 1 year, 1 month ago

Isn't \(C_{10} = 0.123456789101112131415 \ldots\)? I don't see why there'd be a problem with the relation.Log in to reply

But since OP wanted the full formula, you might want to type out that nasty double summation in full. HAHA! – Pi Han Goh · 1 year, 1 month ago

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– Sharky Kesa · 1 year, 1 month ago

Written out the LaTeX hell. Had to put it in large so it could be read.Log in to reply

– Pi Han Goh · 1 year, 1 month ago

My eyes is in pain just by staring at it!Log in to reply

Thanks guys! I love what you guys did! I thought it'd be simpler because this was on an entrance exam for a specialized middle school. – Hobart Pao · 1 year, 1 month ago

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