TOPICS
Search

Copeland-Erdős Constant Continued Fraction


Copeland-ErdosConstantContinuedFraction

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

ChampernowneCopelandErdosCFs

The computed portions of the Champernowne constant continued fraction contain sporadic very large terms (right figure). The illustrated initial terms of the Copeland-Erdős constant continued fraction show no comparable large-term behavior (left figure).

E. Weisstein reported a computation of 1011597392 terms of the continued fraction on Jul. 24, 2013.

Copeland-ErdosConstantContinuedFractionFirstOccurrences

Positions in the continued fraction are counted from 0 at the initial term a_0=0. The positions of the first occurrence of n=1, 2, ... are 7, 15, 19, 1, 6, 14, 11, 3, 16, 253, ... (OEIS A224891). The smallest positive integers reported not to occur in the first 1011597392 terms were 14731, 15456, 15579, 15869, ... (E. Weisstein, Jul. 24, 2013).

The incrementally largest terms in the continued fraction are 0, 4, 8, 16, 18, 58, 87, 484, 1468, 3955, ... (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

Explore with Wolfram|Alpha

References

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

Referenced on Wolfram|Alpha

Copeland-Erdős Constant Continued Fraction

Cite this as:

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

Subject classifications