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 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 Table of n, a(n) for n=2..92. 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. Davis Smith, A Sufficient Condition For Normalcy. 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 Adjacent sequences: A353959 A353960 A353961 * A353963 A353964 A353965 KEYWORD nonn,base,tabl AUTHOR Davis Smith, May 12 2022 STATUS approved

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