cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Joshua Searle

Joshua Searle's wiki page.

Joshua Searle has authored 23 sequences. Here are the ten most recent ones:

A382498 Smallest k such that the fractional part of 1/k is pandigital in base n.

Original entry on oeis.org

3, 5, 13, 7, 11, 11, 11, 43, 17, 13, 17, 19, 17, 19, 79, 23, 29, 23, 23, 23, 31, 47, 31, 73, 29, 29, 41, 41, 41, 47, 37, 43, 41, 37, 137, 59, 47, 47, 47, 47, 59, 47, 47, 47, 67, 59, 53, 241, 53, 53, 59, 71, 59, 59, 59, 67, 73, 61, 73, 67, 71, 67, 383, 71, 79
Offset: 2

Views

Author

Joshua Searle, Mar 29 2025

Keywords

Comments

It appears that for squarefree n, a(n) has a reptend of maximal length and for square n, a(n) has a reptend of half the maximal length.
Not every prime appears in this sequence - excluding 2, the first missing prime is 109.
The first composite term is a(81).
How many times can a term appear consecutively?
How does a(n) grow with n?

Examples

			a(10) = 17 because 1/17 = 0.(0588235294117647)... in base 10 where the brackets indicate the reptend. Every digit 0-9 appears within the reptend and is the smallest unit fraction where this is the case.
a(36) = 137 because 1/137 = 0.(09gjyy5s47cvj6khv9q0ix3xwbk8epr2d4zqjg11u7vsn4gtfi4q9zh2w23ofrla8xmv)... in base 36 where the digits 0-9 and letters a-z have been used as additional digits. Every character appears at least once.

Links

Crossrefs

Cf. A001913, A261773.

A378349 Continued fraction expansion of the base 8 Champernowne constant.

Original entry on oeis.org

0, 6, 7, 1, 842, 5, 11, 2, 1, 4, 1, 12, 1217611913245203113561611289624720261608646275831638269345353220034950193075766082779756144, 39, 1, 13, 19, 1, 1, 2, 1, 6, 1, 4, 9, 1, 2, 1, 3, 2, 1, 223, 2, 1
Offset: 0

Views

Author

Joshua Searle, Dec 14 2024

Keywords

Comments

The next term a(34) is approximately equal to 5.28 * 10^1099.

Links

Crossrefs

Cf. A054634 (base 8 expansion), A378332 (decimal expansion).
Other continued fractions: A066717, A077772, A378345, A378346, A378347, A378348, A378350, A030167.

Programs

  • Mathematica
    ContinuedFraction[ChampernowneNumber[8], 100]

A378348 Continued fraction expansion of the base 7 Champernowne constant.

Original entry on oeis.org

0, 5, 6, 1, 85, 1, 2, 1, 11, 1, 3, 2, 1, 5, 1, 2, 8697444597678755989498288581049684565698396369776180853037564, 1, 4, 2, 8, 6, 1, 2, 11, 1, 11, 1, 9, 2, 11, 1, 13, 2, 3, 10
Offset: 0

Views

Author

Joshua Searle, Dec 14 2024

Keywords

Comments

The next term a(36) is approximately equal to 4.24*10^662.

Links

Crossrefs

Cf. A030998 (base 7 expansion), A378331 (decimal expansion).
Other continued fractions: A066717, A077772, A378345, A378346, A378347, A378349, A378350, A030167.

Programs

  • Mathematica
    ContinuedFraction[ChampernowneNumber[7], 100]

A378350 Continued fraction expansion of the base 9 Champernowne constant.

Original entry on oeis.org

0, 7, 8, 1, 10222, 1, 1, 1, 1, 1, 12, 1, 1, 1, 145, 1, 13127841267973253934598674824559230051317913195904874825561053745645554655306632773083671838234108227370808367172269493508107, 1, 7, 3, 1, 1, 1, 2, 2, 15, 3, 2, 1, 3, 2, 1, 1, 7, 4, 1, 4, 1, 1, 3, 3, 1, 1
Offset: 0

Views

Author

Joshua Searle, Dec 14 2024

Keywords

Links

Crossrefs

Cf. A031076 (base 9 expansion), A378333 (decimal expansion).
Other continued fractions: A066717, A077772, A378345, A378346, A378347, A378348, A378349, A030167.

Programs

  • Mathematica
    ContinuedFraction[ChampernowneNumber[9], 100]

A378345 Continued fraction expansion of the base 4 Champernowne constant.

Original entry on oeis.org

0, 2, 2, 1, 7, 1, 1, 2, 1, 1, 1, 1, 6806293849, 1, 33, 157, 1, 2, 1, 3, 1, 1, 2345427263108642344323518197756649380964709224412095403124301722165, 2, 2, 1, 1, 1, 3, 1, 1, 6, 2, 7, 11, 1, 1, 7, 12, 1, 1, 1, 126, 3, 13, 1, 13, 4, 33, 3, 1, 1, 1, 3, 2, 4, 1, 9, 2
Offset: 0

Views

Author

Joshua Searle, Dec 13 2024

Keywords

Links

Crossrefs

Cf. A030373 (base 4 expansion), A378328 (decimal expansion).
Other continued fractions: A066717, A077772, A378346, A378347, A378348, A378349, A378350, A030167.

Programs

  • Mathematica
    ContinuedFraction[ChampernowneNumber[4], 100]

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

Views

Author

Joshua Searle, Dec 13 2024

Keywords

Comments

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

Links

Crossrefs

Cf. A030548 (base 6 expansion), A378330 (decimal expansion).
Other continued fractions: A066717, A077772, A378345, A378346, A378348, A378349, A378350, A030167.

Programs

  • Mathematica
    ContinuedFraction[ChampernowneNumber[6], 100]

A378346 Continued fraction expansion of the base 5 Champernowne constant.

Original entry on oeis.org

0, 3, 4, 1, 1, 2, 2, 18, 1, 20, 1302701925685142513155, 3, 5, 6, 1, 1, 1, 1, 1, 1, 2, 13, 5, 2, 1, 22, 1, 1
Offset: 0

Views

Author

Joshua Searle, Dec 13 2024

Keywords

Comments

The next term a(28) is approximately equal to 2.83 * 10^173.

Links

Crossrefs

Cf. A031219 (base 5 expansion), A378329 (decimal exapansion).
Other continued fractions: A066717, A077772, A378345, A378347, A378348, A378349, A378350, A030167.

Programs

  • Mathematica
    ContinuedFraction[ChampernowneNumber[5], 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

Views

Author

Joshua Searle, Nov 25 2024

Keywords

Comments

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.

Examples

			0.140624976119696782479669008935663183265457083246828486657555171275414914...

Links

Crossrefs

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).

Programs

  • Mathematica
    First[RealDigits[ChampernowneNumber[9], 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

Views

Author

Joshua Searle, Nov 25 2024

Keywords

Comments

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.

Examples

			0.163264812105216797367094986142605190224237843285462333081380700428319475...

Links

Crossrefs

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).

Programs

  • Mathematica
    First[RealDigits[ChampernowneNumber[8], 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

Views

Author

Joshua Searle, Nov 25 2024

Keywords

Comments

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.

Examples

			0.194435535086240521475840093082908576452932971050422112479588531233679088...

Links

Crossrefs

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).

Programs

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

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.