Prime-Counting Concatenation Constant

Consider the concatenation of the digits of consecutive values of the prime counting function pi(n) for n=1, 2, ..., which gives the terms 0, 01, 012, 0122, 01223, 012233, 0122334, .... Interpreting the limiting sequence as the decimal digits of a constant gives


(OEIS A366033).

Using a method of Szüsz and Volkmann (1994), Campbell (2024) proved that Cramér's conjecture on prime gaps implies the normality of 0.a_1a_2... in a given base b>=2 for a_n=pi(n).

See also

Concatenation Sequence, Consecutive Number Sequences, Copeland-Erdős Constant, Prime Counting Function

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Campbell, J. M. "The Prime-Counting Copeland-Erdős Constant." Acta Math. Hungar. 2024.Sloane, N. J. A. Sequence A366033 in "The On-Line Encyclopedia of Integer Sequences."Szüsz, P. and Volkmann, B. "A Combinatorial Method for Constructing Normal Numbers." Forum Math. 6, 399-414, 1994.

Cite this as:

Weisstein, Eric W. "Prime-Counting Concatenation Constant." From MathWorld--A Wolfram Web Resource.

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