Happy Pi Day!

In America, today's date is written as \(3.14.15\), and at \(9:26:53\) 10 digits of \(\pi\) will appear on watches for the first time in 100 years. Now, in what position in \(\pi\) will the sequence \(1,2,3,4,5\) commence for the first time?

Note: The sequence \(3,1,4,1,5\) commences at position \(1\), \(1,4,1,5,9\) commences at position \(2\), etc.

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