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A054635 Champernowne sequence: write n in base 3 and juxtapose. 22

%I #42 Sep 08 2022 08:45:01

%S 0,1,2,1,0,1,1,1,2,2,0,2,1,2,2,1,0,0,1,0,1,1,0,2,1,1,0,1,1,1,1,1,2,1,

%T 2,0,1,2,1,1,2,2,2,0,0,2,0,1,2,0,2,2,1,0,2,1,1,2,1,2,2,2,0,2,2,1,2,2,

%U 2,1,0,0,0,1,0,0,1,1,0,0,2,1,0,1,0,1,0,1,1,1,0,1,2,1,0,2,0,1,0,2,1

%N Champernowne sequence: write n in base 3 and juxtapose.

%C Essentially the same as A003137. - _R. J. Mathar_, Aug 29 2009

%C An irregular table in which the n-th row lists the base-3 digits of n. - _Jason Kimberley_, Dec 07 2012

%C The base-3 Champernowne constant (A077771): it is normal in base 3. - _Jason Kimberley_, Dec 07 2012

%H Reinhard Zumkeller, <a href="/A054635/b054635.txt">Rows n = 0..1000 of triangle, flattened</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TernaryChampernowneConstant.html">Ternary Champernowne Constant</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Ternary_numeral_system">Ternary numeral system</a>

%t almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; Array[ almostNatural[#, 3] &, 105, 0] (* _Robert G. Wilson v_, Jun 29 2014 *)

%o (Magma) [0]cat &cat[Reverse(IntegerToSequence(n,3)):n in[1..31]]; // _Jason Kimberley_, Dec 07 2012

%o (Haskell)

%o a054635 n k = a054635_tabf !! n !! k

%o a054635_row n = a054635_tabf !! n

%o a054635_tabf = map reverse a030341_tabf

%o a054635_list = concat a054635_tabf

%o -- _Reinhard Zumkeller_, Feb 21 2013

%o (Python)

%o from sympy.ntheory.digits import digits

%o def agen(limit):

%o for n in range(limit):

%o yield from digits(n, 3)[1:]

%o print([an for an in agen(35)]) # _Michael S. Branicky_, Sep 01 2021

%Y Cf. A054637 (partial sums).

%Y Cf. A081604 (row lengths), A053735 (row sums), A030341 (rows reversed), A007089, A077771.

%Y Table in which the n-th row lists the base b digits of n: A030190 and A030302 (b=2), A003137 and this sequence (b=3), A030373 (b=4), A031219 (b=5), A030548 (b=6), A030998 (b=7), A031035 and A054634 (b=8), A031076 (b=9), A007376 and A033307 (b=10). - _Jason Kimberley_, Dec 06 2012

%K nonn,base,cons,easy,tabf

%O 0,3

%A _N. J. A. Sloane_, Apr 16 2000

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Last modified April 23 23:26 EDT 2024. Contains 371917 sequences. (Running on oeis4.)