A030548 -id:A030548 - cp's OEIS frontend

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

N. J. A. Sloane, Apr 16 2000

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

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

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

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

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

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 *)

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

A378347 Continued fraction expansion of the base 6 Champernowne constant.

Original entry on oeis.org

0, 4, 5, 1, 10, 1, 4, 3, 9, 1, 2, 2, 1, 1, 699745284439054751106354294914368414245, 2, 5, 1, 20, 22, 2, 2, 1, 10, 3, 1, 2, 2, 2, 1, 1, 2, 1, 1

Offset: 0

Joshua Searle, Dec 13 2024

The next term a(34) is approximately equal to 1.21 * 10^364.

OeisWiki, Champernowne constant

Cf. A030548 (base 6 expansion), A378330 (decimal expansion).

Other continued fractions: A066717, A077772, A378345, A378346, A378348, A378349, A378350, A030167.

ContinuedFraction[ChampernowneNumber[6], 100]

A378328 Decimal expansion of the base 4 Champernowne constant.

Original entry on oeis.org

4, 2, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 6, 5, 7, 6, 4, 5, 5, 6, 5, 7, 1, 4, 2, 0, 1, 6, 1, 9, 8, 5, 0, 9, 5, 5, 4, 6, 2, 3, 8, 9, 6, 7, 2, 3, 0, 4, 1, 0, 6, 8, 2, 7, 9, 1, 6, 3, 5, 1, 7, 2, 5, 8, 7, 5, 5, 3, 5, 3, 9, 9, 3, 4, 4, 9, 2, 3, 1, 5, 4, 4, 4

Offset: 0

Joshua Searle, Nov 23 2024

This constant is formed by the concatenation of the natural numbers in base 4 and then converted into base 10.

This constant is 4-normal.

			0.426111111111111065764556571420161985095546238967230410682791635172587553...

OeisWiki, Champernowne constant

Cf. A030302, A003137, A030373, A031219, A030548, A030998, A054634, A031076, A033307 (base n expansions of base n Champernowne constants, without leading zero, for 2 <= n <= 10).
Cf. A066716, A077771, A378328, A378329, A378330, A378331, A378332, A378333, A033307 (decimal expansions of base n Champernowne constants for 2 <= n <= 10).
Cf. A066717, A077772, A378345, A378346, A378347, A378348, A378349, A378350, A030167 (continued fraction expansions of base n Champernowne constants for 2 <= n <= 10).

First[RealDigits[ChampernowneNumber[4], 10, 100]]

A378329 Decimal expansion of the base 5 Champernowne constant.

Original entry on oeis.org

3, 1, 0, 7, 3, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 6, 3, 0, 3, 3, 3, 1, 1, 6, 0, 4, 9, 4, 4, 8, 4, 9, 1, 1, 5, 5, 0, 4, 6, 8, 2, 6, 2, 2, 2, 6, 8, 4, 7, 0, 3, 4, 3, 3, 9, 2, 2, 9, 9, 6, 8, 7, 8, 2, 5, 1, 8, 2, 1, 0, 1

Offset: 0

Joshua Searle, Nov 23 2024

This constant is formed by the concatenation of the natural numbers in base 5 and then converted into base 10.

This constant is 5-normal.

			0.310736111111111111111111111110963033311604944849115504682622268470343392...

OeisWiki, Champernowne constant

Cf. A030302, A003137, A030373, A031219, A030548, A030998, A054634, A031076, A033307 (base n expansions of base n Champernowne constants, without leading zero, for 2 <= n <= 10).
Cf. A066716, A077771, A378328, A378329, A378330, A378331, A378332, A378333, A033307 (decimal expansions of base n Champernowne constants for 2 <= n <= 10).
Cf. A066717, A077772, A378345, A378346, A378347, A378348, A378349, A378350, A030167 (continued fraction expansions of base n Champernowne constants for 2 <= n <= 10).

First[RealDigits[ChampernowneNumber[5], 10, 100]]

A378330 Decimal expansion of the base 6 Champernowne constant.

Original entry on oeis.org

2, 3, 9, 8, 6, 2, 6, 8, 5, 8, 1, 5, 0, 6, 6, 7, 6, 7, 4, 4, 7, 7, 1, 9, 8, 2, 8, 6, 7, 2, 2, 0, 9, 6, 2, 4, 5, 9, 0, 5, 7, 6, 9, 7, 1, 5, 2, 9, 3, 5, 0, 2, 1, 3, 7, 6, 0, 6, 9, 3, 1, 9, 5, 6, 3, 1, 5, 7, 6, 5, 8, 3, 4, 3, 7, 7, 5, 4, 8, 3, 0, 5, 0, 7, 8, 0, 4

Offset: 0

Joshua Searle, Nov 23 2024

This constant is formed by the concatenation of the natural numbers in base 6 and then converted into base 10.

This constant is 6-normal.

			0.239862685815066767447719828672209624590576971529350213760693195631576583...

OeisWiki, Champernowne constant

Cf. A030302, A003137, A030373, A031219, A030548, A030998, A054634, A031076, A033307 (base n expansions of base n Champernowne constants, without leading zero, for 2 <= n <= 10).
Cf. A066716, A077771, A378328, A378329, A378330, A378331, A378332, A378333, A033307 (decimal expansions of base n Champernowne constants for 2 <= n <= 10).
Cf. A066717, A077772, A378345, A378346, A378347, A378348, A378349, A378350, A030167 (continued fraction expansions of base n Champernowne constants for 2 <= n <= 10).

First[RealDigits[ChampernowneNumber[6], 10, 100]]

A378331 Decimal expansion of the base 7 Champernowne constant.

Original entry on oeis.org

1, 9, 4, 4, 3, 5, 5, 3, 5, 0, 8, 6, 2, 4, 0, 5, 2, 1, 4, 7, 5, 8, 4, 0, 0, 9, 3, 0, 8, 2, 9, 0, 8, 5, 7, 6, 4, 5, 2, 9, 3, 2, 9, 7, 1, 0, 5, 0, 4, 2, 2, 1, 1, 2, 4, 7, 9, 5, 8, 8, 5, 3, 1, 2, 3, 3, 6, 7, 9, 0, 8, 8, 7, 3, 9, 4, 0, 3, 5, 6, 6, 3, 9, 7, 0, 8, 5

Offset: 0

Joshua Searle, Nov 25 2024

This constant is formed by the concatenation of the natural numbers in base 7 and then converted into base 10.

This constant is 7-normal.

			0.194435535086240521475840093082908576452932971050422112479588531233679088...

OeisWiki, Champernowne constant

Cf. A030302, A003137, A030373, A031219, A030548, A030998, A054634, A031076, A033307
(base n expansions of base n Champernowne constants, without leading zero, for 2 <= n <= 10).
Cf. A066716, A077771, A378328, A378329, A378330, A378331, A378332, A378333, A033307 (decimal expansions of base n Champernowne constants for 2 <= n <= 10).
Cf. A066717, A077772, A378345, A378346, A378347, A378348, A378349, A378350, A030167 (continued fraction expansions of base n Champernowne constants for 2 <= n <= 10).

First[RealDigits[ChampernowneNumber[7], 10, 100]]

A378332 Decimal expansion of the base 8 Champernowne constant.

Original entry on oeis.org

1, 6, 3, 2, 6, 4, 8, 1, 2, 1, 0, 5, 2, 1, 6, 7, 9, 7, 3, 6, 7, 0, 9, 4, 9, 8, 6, 1, 4, 2, 6, 0, 5, 1, 9, 0, 2, 2, 4, 2, 3, 7, 8, 4, 3, 2, 8, 5, 4, 6, 2, 3, 3, 3, 0, 8, 1, 3, 8, 0, 7, 0, 0, 4, 2, 8, 3, 1, 9, 4, 7, 5, 9, 3, 8, 5, 2, 3, 5, 5, 7, 5, 7, 1, 1, 7, 6

Offset: 0

Joshua Searle, Nov 25 2024

This constant is formed by the concatenation of the natural numbers in base 8 and then converted into base 10.

This constant is 8-normal.

			0.163264812105216797367094986142605190224237843285462333081380700428319475...

OeisWiki, Champernowne constant

Cf. A030302, A003137, A030373, A031219, A030548, A030998, A054634, A031076, A033307 (base n expansions of base n Champernowne constants, without leading zero, for 2 <= n <= 10).
Cf. A066716, A077771, A378328, A378329, A378330, A378331, A378332, A378333, A033307 (decimal expansions of base n Champernowne constants for 2 <= n <= 10).
Cf. A066717, A077772, A378345, A378346, A378347, A378348, A378349, A378350, A030167 (continued fraction expansions of base n Champernowne constants for 2 <= n <= 10).

First[RealDigits[ChampernowneNumber[8], 10, 100]]

A378333 Decimal expansion of the base 9 Champernowne constant.

Original entry on oeis.org

1, 4, 0, 6, 2, 4, 9, 7, 6, 1, 1, 9, 6, 9, 6, 7, 8, 2, 4, 7, 9, 6, 6, 9, 0, 0, 8, 9, 3, 5, 6, 6, 3, 1, 8, 3, 2, 6, 5, 4, 5, 7, 0, 8, 3, 2, 4, 6, 8, 2, 8, 4, 8, 6, 6, 5, 7, 5, 5, 5, 1, 7, 1, 2, 7, 5, 4, 1, 4, 9, 1, 4, 8, 7, 8, 1, 8, 5, 4, 9, 5, 2, 4, 3, 6, 4, 4

Offset: 0

Joshua Searle, Nov 25 2024

This constant is formed by the concatenation of the natural numbers in base 9 and then converted into base 10.

This constant is 9-normal.

			0.140624976119696782479669008935663183265457083246828486657555171275414914...

OeisWiki, Champernowne constant

Cf. A030302, A003137, A030373, A031219, A030548, A030998, A054634, A031076, A033307 (base n expansions of base n Champernowne constants, without leading zero, for 2 <= n <= 10).
Cf. A066716, A077771, A378328, A378329, A378330, A378331, A378332, A378333, A033307 (decimal expansions of base n Champernowne constants for 2 <= n <= 10).
Cf. A066717, A077772, A378345, A378346, A378347, A378348, A378349, A378350, A030167 (continued fraction expansions of base n Champernowne constants for 2 <= n <= 10).

First[RealDigits[ChampernowneNumber[9], 10, 100]]

A030575 Run length of n-th run of digit 0 in A030567.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Clark Kimberling

Differs from A030556 whenever a base 6 sequence of a number is inserted which has a non-palindromic sequence of run-lengths of 0. Happens first scanning 10010_6 = 1302_10 which is inserted in A030567 as 01001 (run lengths 1,2) but in A030548 as 10010 (run lengths 2,1). - R. J. Mathar, Jul 23 2025 and Andrei Zabolotskii

R. J. Mathar, Table of n, a(n) for n = 1..805

Initial 1 inserted for consistency with change in A030567 and more terms from Sean A. Irvine, Apr 03 2020

A275993 Champernowne sequence: write n in base 16 and juxtapose.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 11, 1, 12, 1, 13, 1, 14, 1, 15, 2, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 2, 10, 2, 11, 2, 12, 2, 13, 2, 14, 2, 15, 3, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 3, 10, 3, 11, 3

Offset: 0

Robert G. Wilson v, Aug 15 2016

10 -> A, 11 -> B, 12 -> C, 13 -> D, 14 -> E & 15 -> F.

Paolo Xausa, Table of n, a(n) for n = 0..10000
Jim Bumgardner, Hexadecimal Sudoku Puzzles
Tech Insider, This is the code Matt Damon and NASA use to communicate in 'The Martian'
Eric W. Weisstein, Wolfram MathWorld, Hexadecimal
Wikipedia, Hexadecimal

Tables in which the n-th row lists the base b digits of n: A030190 and A030302 (b=2), A003137 and A054635 (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).

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[#, 16] &, 105, 0]
First[RealDigits[ChampernowneNumber[16], 16, 100, 0]] (* Paolo Xausa, Jun 21 2024 *)

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Magma

Mathematica

Python

A378347 Continued fraction expansion of the base 6 Champernowne constant.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A378328 Decimal expansion of the base 4 Champernowne constant.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A378329 Decimal expansion of the base 5 Champernowne constant.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A378330 Decimal expansion of the base 6 Champernowne constant.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A378331 Decimal expansion of the base 7 Champernowne constant.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A378332 Decimal expansion of the base 8 Champernowne constant.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A378333 Decimal expansion of the base 9 Champernowne constant.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs