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Copeland-Erdős Constant Continued Fraction


Copeland-ErdosConstantContinuedFraction

The first few terms of the continued fraction of the Copeland-Erdős constant are [0; 4, 4, 8, 16, 18, 5, 1, ...] (OEIS A030168), illustrated above.

ChampernowneCopelandErdosCFs

Interestingly, while the Champernowne constant continued fraction contains sporadic very large terms (right figure), making the continued fraction difficult to calculate, the Copeland-Erdős constant has a well-behaved continued fraction that does not show the "large term" phenomenon (left figure).

E. Weisstein computed 1011597392 terms of the continued fraction on Jul. 24, 2013.

Copeland-ErdosConstantContinuedFractionFirstOccurrences

The positions of the first occurrence of n=1, 2, ... in the continued fraction are 7, 15, 19, 1, 6, 14, 11, 3, 16, 253, ... (OEIS A224891). Smallest numbers not occurring in the first 1,011,597,392 terms of the continued fraction are 14731, 15456, 15579, 15869, ... (E. Weisstein, Jul. 24, 2013).

The incrementally largest terms are 4, 8, 16, 18, 58, 87, 484, ... (OEIS A033310), which occur at positions 0, 1, 3, 4, 5, 17, 35, 71, 88, 1556, ... (OEIS A224890).


See also

Copeland-Erdős Constant, Copeland-Erdős Constant Digits

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References

Sloane, N. J. A. Sequences A030168, A033310, A224890, and A224891 in "The On-Line Encyclopedia of Integer Sequences."

Cite this as:

Weisstein, Eric W. "Copeland-Erdős Constant Continued Fraction." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Copeland-ErdosConstantContinuedFraction.html

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