A030167 -id:A030167 - cp's OEIS frontend

A378328 Decimal expansion of the base 4 Champernowne constant.

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]]

A033435 Continued fraction for Champernowne constant = 0.01234567891011121314...

Original entry on oeis.org

0, 81, 1490845, 2, 5, 2, 1, 11, 1, 1, 1, 5, 1, 1, 1, 1

Offset: 0

N. J. A. Sloane

Cf. A033307, A030167.

ContinuedFraction[With[{nn=20,c=Flatten[IntegerDigits/@Range[0,nn]]}, N[ FromDigits[ c]/10^Length[c],Length[c]]],16] (* Harvey P. Dale, Apr 10 2013 *)

Next term is very large.

A066700 The leading digits in the terms in A067103 converge; dividing by a suitable power of 10 they converge to the number shown below; sequence gives continued fraction for this number.

Original entry on oeis.org

1, 2, 12, 4, 34, 1, 22, 1, 4, 1, 1, 2, 1, 1, 17, 16, 3, 1, 1, 2, 1, 1, 1, 5, 1, 1, 3, 3, 14, 2, 107, 1, 1, 8, 5, 4, 7, 1, 4, 1, 6, 3, 19, 3, 1, 1, 2, 3, 5, 76, 1, 1, 2, 1, 1, 90, 2, 2, 48717, 1, 1, 1, 3, 1, 1, 2, 4, 1, 1, 1, 14, 2, 1, 1, 2, 4, 28, 2, 3, 46, 1, 1, 3, 1, 1, 1, 2, 1, 5, 12, 1, 1, 3, 3, 1, 2, 3, 1, 78, 1, 1, 1, 3, 2, 4, 1, 6, 1, 1, 1048, 1, 3, 1, 1, 2, 3, 4, 1, 2, 4, 3, 8, 1, 12, 5, 1, 1, 7, 1, 11, 11, 1, 118, 6, 1, 2, 1, 5, 3, 1, 1, 1, 2, 3, 1, 2, 1, 1, 2, 2, 3, 5, 4, 1, 12, 147838832589501802758390, 1, 10, 1, 1, 1, 2, 4, 6, 10, 2, 8, 1, 2, 1, 1, 7, 1, 1, 1, 3, 9, 1, 1, 1, 55, 1, 1, 1, 1, 2

Offset: 1

Randall L Rathbun, Jan 12 2002

			1.480389426511475059423875475946678140937510326102334419703757169...

Cf. A007908, A019522, A067103.

For a more dramatic continued fraction see A030167.

{A067103(n)= c=0; d=0; for(i=1,n, c=c*10^(1+floor(3*log(i)/log(10)))+i^3; d=d*10^(1+floor(log(i)/log(10)))+i; ); floor(c/d) }

c1(n) = my(s=""); for(k=1, n, s=Str(s, k)); eval(s); \\ A007908
c3(n) = my(s=""); for(k=1, n, s=Str(s, k^3)); eval(s); \\ A019522
lista() = my(nn=1000); default(realprecision, 1000); my(x=c3(nn)\c1(nn)); x = x/10.^(#Str(x)-1); contfrac(x); \\ Michel Marcus, May 25 2022

A293577 Decimal expansion of number with continued fraction expansion 0, 1, 12, 123, 1234, 12345, 123456, ... (A007908).

Original entry on oeis.org

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

Offset: 0

Ilya Gutkovskiy, Oct 12 2017

			0.92312499968345024117401233060984219166367488... = 1/(1 + 1/(12 + 1/(123 + 1/(1234 + 1/(12345 + 1/(123456 + 1/...)))))).

G. C. Greubel, Table of n, a(n) for n = 0..5000 [a(5000) corrected by _Georg Fischer_, Apr 02 2025]

Cf. A007908, A030167, A052119, A264934.

Take[RealDigits[N[FromContinuedFraction[Table[FromDigits[Flatten[IntegerDigits[Range[n]]]], {n, 0, 20}]], 101]][[1]], 100]  (* modified by Ilya Gutkovskiy, Nov 08 2017 *)

a(99) corrected by G. C. Greubel, Nov 07 2017

A365237 Decimal expansion of 1/A033307 (decimal Champernowne constant).

Original entry on oeis.org

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

Offset: 1

Kelvin Voskuijl, Aug 27 2023

Appears to coincide with A090903 from the 10th digit onwards.

			8.10000006707603361330731967383416787753583647347857972252510...

Cf. A031310, A033307.
Cf. A030167 (continued fraction).
Cf. A365238 (reciprocal of binary Champernowne constant).

RealDigits[1/ChampernowneNumber[10] , 10, 120][[1]]

cp's OEIS Frontend

A378328 Decimal expansion of the base 4 Champernowne constant.

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A378329 Decimal expansion of the base 5 Champernowne constant.

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A378330 Decimal expansion of the base 6 Champernowne constant.

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Mathematica

A378331 Decimal expansion of the base 7 Champernowne constant.

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A378332 Decimal expansion of the base 8 Champernowne constant.

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A378333 Decimal expansion of the base 9 Champernowne constant.

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A033435 Continued fraction for Champernowne constant = 0.01234567891011121314...

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Extensions

A066700 The leading digits in the terms in A067103 converge; dividing by a suitable power of 10 they converge to the number shown below; sequence gives continued fraction for this number.

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PARI

A293577 Decimal expansion of number with continued fraction expansion 0, 1, 12, 123, 1234, 12345, 123456, ... (A007908).

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