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# Champernowne Constant Digits

The Champernowne constant has decimal expansion

(OEIS A033307).

The Earls sequence (starting position of copies of the digit ) for is given for , 2, ... by 1, 34, 56, 1222, 1555, 25554, 29998, 433330, 7988888882, 1101010101010, ... (OEIS A224896).

The starting positions of the first occurrence of , 1, 2, ... in the decimal expansion of (not including the initial 0 to the left of the decimal point) are 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 1, ... (OEIS A229186).

Scanning the decimal expansion of until all -digit numbers have occurred, the last 1-, 2-, ... digit numbers appearing are 0, 00, 000, 0000, ..., which end at digits 11, 192, 2893, 38894, 488895, ... (OEIS A072290).

The digit sequence 0123456789 first occurs at positions 11234567799, 22345677908, 33456779017, 44567790126, 55677901235, 66779012344, ... (OEIS A000000) and 9876543210 at positions 7777777779, 9876543212, 19987654323, 30998765434, 42099876545, 53209987656, 64320998767, ... (OEIS A000000; E. Weisstein, Jul. 26, 2013).

-constant primes occur for 10, 14, 24, 235, 2804, 4347, 37735, ... (OEIS A071620) digits.

It is known that the Champernowne constant is normal in base 10 (Champernowne 1933, Bailey and Crandall 2002), though the following table giving the counts of digits in the first terms shows non-normal behavior up to at least due to an excess of 1s and surfeit of 0s when cutting the digit string off at locations such as .

 OEIS 10 100 0 A000000 0 5 66 747 8642 83528 884151 9234568 96021948 1 A000000 2 16 177 1858 19753 179810 1582562 14234568 130589850 2 A000000 1 16 177 1636 11111 94539 995260 10345679 100589849 3 A000000 1 16 148 858 8642 94539 995161 10234568 96589849 4 A000000 1 16 77 858 8642 94539 995160 9345679 96089849 5 A000000 1 11 77 858 8642 93723 982462 9345679 96029849 6 A000000 1 5 77 858 8642 93538 895160 9345679 96022849 7 A000000 1 5 67 833 8642 93538 894462 9345679 96022049 8 A000000 1 5 67 747 8642 88718 891462 9333333 96021959 9 A000000 1 5 67 747 8642 83528 884160 9234568 96021949

## See also

Champernowne Constant, Champernowne Constant Continued Fraction, Constant Digit Scanning, Constant Primes, Earls Sequence, Smarandache Number

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## References

Champernowne, D. G. "The Construction of Decimals Normal in the Scale of Ten." J. London Math. Soc. 8, 1933.Bailey, D. H. and Crandall, R. E. "Random Generators and Normal Numbers." Exper. Math. 11, 527-546, 2002.Sloane, N. J. A. Sequences A071620, A072290, A224896, and A229186 in "The On-Line Encyclopedia of Integer Sequences."

## Cite this as:

Weisstein, Eric W. "Champernowne Constant Digits." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChampernowneConstantDigits.html