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Copeland-Erdős Constant

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The Copeland-Erdős constant is the constant with decimal expansion 0.23571113171923... (OEIS A033308) obtained by concatenating consecutive primes: 2, 23, 235, 2357, 235711, ... (OEIS A019518). It is one of the Smarandache sequences and is considered as an infinite word by Allouche and Shallit (2003, pp. 299 and 334).

It is therefore given by the formula

C_(CE)=sum_(n=1)^infty(p_n)/(10^(sum_(k=1)^(n)|_log_(10)p_k_|+n)).

Copeland and Erdős (1946) showed that it is a normal number in base 10.

Interestingly, while the Champernowne constant continued fraction contains sporadic very large terms, making the continued fraction difficult to calculate, the Copeland-Erdős constant continued fraction is well-behaved and does not show the "large term" phenomenon.

See also

Champernowne Constant, Copeland-Erdős Constant Continued Fraction, Copeland-Erdős Constant Digits, Prime-Counting Concatenation Constant, Prime Number

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References

Allouche, J.-P. and Shallit, J. Automatic Sequences: Theory, Applications, Generalizations. Cambridge, England: Cambridge University Press, 2003.Bailey, D. H. and Crandall, R. E. "Random Generators and Normal Numbers." Exper. Math. 11, 527-546, 2002.Champernowne, D. G. "The Construction of Decimals Normal in the Scale of Ten." J. London Math. Soc. 8, 1933.Copeland, A. H. and Erdős, P. "Note on Normal Numbers." Bull. Amer. Math. Soc. 52, 857-860, 1946.Pickover, C. A. The Mathematics of Oz: Mental Gymnastics from Beyond the Edge. New York: Cambridge University Press, p. 284, 2002.Sloane, N. J. A. Sequences A019518, A030168, A033308, A033309, A033310, and A224890 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Copeland-Erdős Constant

Cite this as:

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

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