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

0,3

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.

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.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000720, A001191, A033307, A033308.

Sequence in context: A237819 A082447 A139789 * A000720 A230980 A070549

Adjacent sequences: A366030 A366031 A366032 * A366034 A366035 A366036

Keyword

nonn,cons,base

Author

John M. Campbell, Sep 26 2023

Status

approved