A366033 Successive digits of consecutive terms of the prime-counting function A000720.

0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 3, 1, 4, 1, 4, 1, 4, 1, 4, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6

Offset: 0

Author

John M. Campbell, Sep 26 2023

Keywords

• nonn
• cons
• base

Comments

By analogy with the Copeland-Erdős constant 0.2357111317... given by concatenating the base-10 expansions of consecutive entries of the sequence of prime numbers, the so-called "prime-counting Copeland-Erdős constant" 0.0122...9101011... is defined similarly, but with the use of the prime-counting function in place of the prime number sequence.

Examples

			0.012233444455666677888899999910101111...
The prime-counting function evaluated at 1 is 0, so a(0) = 0, and the first digit after the decimal point of the prime-counting Copeland-Erdős constant is 0.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000
• John M. Campbell, The prime-counting Copeland-Erdős constant, arXiv:2309.13520 [math.NT], 2023.
• Eric Weisstein's World of Mathematics, Consecutive Number Sequences.
• Eric Weisstein's World of Mathematics, Prime-Counting Concatenation Constant.

Crossrefs

Cf. A000720, A001191, A033307, A033308.

Programs

Mathematica

Flatten[Table[IntegerDigits[PrimePi[n]], {n, 1, 57}]]
Flatten[IntegerDigits[PrimePi[Range[57]]]] (* Eric W. Weisstein, Jun 07 2024 *)

PARI

concat(0, concat(vector(50, i, digits(primepi(i))))) \\ Michel Marcus, Nov 04 2023