login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A353962 Square array read by descending antidiagonals: The n-th row gives the decimal expansion of the base-n Champernowne constant. 2
8, 6, 5, 2, 9, 4, 2, 8, 2, 3, 4, 9, 6, 1, 2, 0, 5, 1, 0, 3, 1, 1, 8, 1, 7, 9, 9, 1, 2, 1, 1, 3, 8, 4, 6, 1, 5, 6, 1, 6, 6, 4, 3, 4, 1, 8, 7, 1, 1, 2, 3, 2, 0, 2, 1, 6, 5, 1, 1, 6, 5, 6, 6, 3, 0, 0, 8, 3, 1, 1, 8, 5, 4, 2, 4, 9, 9, 0, 0, 8, 1, 1, 5, 3, 8, 4, 5, 9, 9, 9, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
The base-n Champernowne constant (C_n) is normal in base n. A(n,k) is the (k+1)-th decimal digit of the fractional part of C_n.
LINKS
Verónica Becher and Santiago Figueira, An example of a computable absolutely normal number, Theoretical Computer Science, 270 (2002), 947-958.
Arthur H. Copeland and Paul Erdős, Note on normal numbers, Bull. Amer. Math. Soc. 52 (1946), 857-860.
Davar Khoshnevisan, Normal Numbers are Normal, Clay Mathematics Institute Annual Report, 2006, 15-31.
Ivan Niven and H.S. Zuckerman, On The Definition of Normal Numbers, Pacific J. Math., 1 (1951), 103-109.
FORMULA
A(n,k) = floor(C_n*10^(k+1)) mod 10 where C_n (the base-n Champernowne constant) = Sum_{i>=1} i/(n^(i + Sum_{k=1..i-1} floor(log_m(k+1))).
EXAMPLE
The square array A(n,k) begins:
n/k | 0 1 2 3 4 5 6 7 8 9 10 11 ...
----+---------------------------------------
2 | 8 6 2 2 4 0 1 2 5 8 6 8 ...
3 | 5 9 8 9 5 8 1 6 7 5 3 8 ...
4 | 4 2 6 1 1 1 1 1 1 1 1 1 ...
5 | 3 1 0 7 3 6 1 1 1 1 1 1 ...
6 | 2 3 9 8 6 2 6 8 5 8 1 5 ...
7 | 1 9 4 4 3 5 5 3 5 0 8 6 ...
8 | 1 6 3 2 6 4 8 1 2 1 0 5 ...
9 | 1 4 0 6 2 4 9 7 6 1 1 9 ...
10 | 1 2 3 4 5 6 7 8 9 1 0 1 ...
...
MATHEMATICA
A[n_, k_]:=Mod[Floor[ChampernowneNumber[n]10^(k + 1)] , 10]; Flatten[Table[Reverse[Table[A[n-k, k], {k, 0, n-2}]], {n, 2, 14}]] (* Stefano Spezia, May 13 2022 *)
CROSSREFS
Rows: A066716 (n=2), A077771 (n=3), A033307 (n=10).
Cf. A063945.
Sequence in context: A011329 A092033 A061360 * A120818 A125579 A202258
KEYWORD
nonn,base,tabl
AUTHOR
Davis Smith, May 12 2022
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 15 20:47 EDT 2024. Contains 371696 sequences. (Running on oeis4.)