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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`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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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.Log in to reply

So,

\[T_n = \lfloor 10^{n} \times C_{10} \rfloor \pmod{10}\]

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AKA

\[\large T_k = \left \lfloor 10^k \times \displaystyle \sum_{m=0}^{\infty} \sum_{n=10^{m-1}}^{10^m - 1} \dfrac {n}{10^{m(n - 10^{m - 1} + 1) + 9 \sum_{l=1}^{m-1} 10^{l-1} l}} \right \rfloor \pmod{10}\]

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Comment deleted Oct 25, 2015

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But since OP wanted the full formula, you might want to type out that nasty double summation in full. HAHA!

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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.

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