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%I #51 Jun 23 2022 08:11:49
%S 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,
%T 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,
%U 1,1,8,5,4,2,4,9,9,0,0,8,1,1,5,3,8,4,5,9,9,9,0
%N Square array read by descending antidiagonals: The n-th row gives the decimal expansion of the base-n Champernowne constant.
%C 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.
%H Verónica Becher and Santiago Figueira, <a href="https://doi.org/10.1016/S0304-3975(01)00170-0">An example of a computable absolutely normal number</a>, Theoretical Computer Science, 270 (2002), 947-958.
%H Arthur H. Copeland and Paul Erdős, <a href="https://doi.org/10.1090/S0002-9904-1946-08657-7">Note on normal numbers</a>, Bull. Amer. Math. Soc. 52 (1946), 857-860.
%H Davar Khoshnevisan, <a href="https://www.claymath.org/library/annual_report/ar2006/06report_normalnumbers.pdf">Normal Numbers are Normal</a>, Clay Mathematics Institute Annual Report, 2006, 15-31.
%H Ivan Niven and H.S. Zuckerman, <a href="https://msp.org/pjm/1951/1-1/pjm-v1-n1-s.pdf#page=105">On The Definition of Normal Numbers</a>, Pacific J. Math., 1 (1951), 103-109.
%H Davis Smith, <a href="/A353962/a353962_3.txt">A Sufficient Condition For Normalcy.</a>
%F 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))).
%e The square array A(n,k) begins:
%e n/k | 0 1 2 3 4 5 6 7 8 9 10 11 ...
%e ----+---------------------------------------
%e 2 | 8 6 2 2 4 0 1 2 5 8 6 8 ...
%e 3 | 5 9 8 9 5 8 1 6 7 5 3 8 ...
%e 4 | 4 2 6 1 1 1 1 1 1 1 1 1 ...
%e 5 | 3 1 0 7 3 6 1 1 1 1 1 1 ...
%e 6 | 2 3 9 8 6 2 6 8 5 8 1 5 ...
%e 7 | 1 9 4 4 3 5 5 3 5 0 8 6 ...
%e 8 | 1 6 3 2 6 4 8 1 2 1 0 5 ...
%e 9 | 1 4 0 6 2 4 9 7 6 1 1 9 ...
%e 10 | 1 2 3 4 5 6 7 8 9 1 0 1 ...
%e ...
%t 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 *)
%Y Rows: A066716 (n=2), A077771 (n=3), A033307 (n=10).
%Y Cf. A063945.
%K nonn,base,tabl
%O 2,1
%A _Davis Smith_, May 12 2022
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