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

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, 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, 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

Offset: 0

Author

N. J. A. Sloane, Apr 16 2000

Keywords

• nonn
• base
• cons
• easy
• tabf

Comments

Essentially the same as A003137. - R. J. Mathar, Aug 29 2009

An irregular table in which the n-th row lists the base-3 digits of n. - Jason Kimberley, Dec 07 2012

The base-3 Champernowne constant (A077771): it is normal in base 3. - Jason Kimberley, Dec 07 2012

Links

• Reinhard Zumkeller, Rows n = 0..1000 of triangle, flattened
• Eric Weisstein's World of Mathematics, Ternary Champernowne Constant
• Wikipedia, Ternary numeral system

Crossrefs

Cf. A054637 (partial sums).

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

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

Programs

Haskell

a054635 n k = a054635_tabf !! n !! k
a054635_row n = a054635_tabf !! n
a054635_tabf = map reverse a030341_tabf
a054635_list = concat a054635_tabf
-- Reinhard Zumkeller, Feb 21 2013

Magma

[0]cat &cat[Reverse(IntegerToSequence(n,3)):n in[1..31]]; // Jason Kimberley, Dec 07 2012

Mathematica

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 *)
First[RealDigits[ChampernowneNumber[3], 3, 100, 0]] (* Paolo Xausa, Jun 19 2024 *)

Python

from sympy.ntheory.digits import digits
def agen(limit):
    for n in range(limit):
        yield from digits(n, 3)[1:]
print([an for an in agen(35)]) # Michael S. Branicky, Sep 01 2021