Champernowne's constant C₁₀ = 0.123456789101112131415... formed by concatenating all positive integers. It's transcendental and normal in base 10 (every digit sequence appears with expected frequency). Finding the n-th digit requires knowing how many digits 1-digit, 2-digit, ... numbers contribute.
How to Use
Enter position n:
- Digit: The n-th digit of C₁₀
- Number: Which integer contains it
- Context: Surrounding digits
Finding the n-th Digit
1-digit numbers: 9 numbers × 1 digit = 9 digits. 2-digit: 90 × 2 = 180. d-digit: 9×10^(d-1) × d. Subtract group sizes to find which group, then which number, then which digit within the number.
Properties
- Transcendental (Mahler, 1937)
- Normal in base 10 (Champernowne, 1933)
- Continued fraction has unbounded terms
- Generalizes to any base b
Step-by-Step Instructions
- 1Enter position.
- 2View digit.
- 3See context.
- 4Identify number.
- 5Explore sequence.