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www.mikescher.com/www/statics/euler/euler_040_explanation.md
2017-11-08 17:39:51 +01:00

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This one is really great - I came up with an O(log n) algorithm (crazy fast) for determining the n-th digit.
First I tested it in LinqPad, so here the C# code for the algorithm:
```csharp
public int digitAt(int pos) {
int digitcount = 1;
int digitvalue = 1;
// Get DigitCount of current number
while(pos > digitvalue * 9 * digitcount) {
pos -= digitvalue * 9 * digitcount;
digitcount++;
digitvalue *= 10;
}
// current number and digit-position in number
int value = digitvalue + (pos - 1)/digitcount;
int digit = digitcount - (pos - 1)%digitcount - 1;
return getInternalDigit(value, digit);
}
public int getInternalDigit(int value, int digit) {
return (value / (int)Math.Pow(10, digit)) % 10;
}
```