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.

Previous Showing 11-20 of 20 results.

A154859 Decimal expansion of log_9 (17).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			1.2894509615812829467581871223200888222408771473697233947468...

Links

Crossrefs

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), this sequence, A154947 (m=18), A155061 (m=19), A155503 (m=20), A155676 (m=21), A155743 (m=22), A155829 (m=23), A155976 (m=24).

Programs

  • Magma
    SetDefaultRealField(RealField(100)); Log(17)/Log(9); // G. C. Greubel, Sep 01 2018
  • Mathematica
    RealDigits[Log[9, 17], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)
  • PARI
    default(realprecision, 100); log(17)/log(9) \\ G. C. Greubel, Sep 01 2018

A154947 Decimal expansion of log_9 (18).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			1.3154648767857287185497635571713804271497928200659402139353...

Links

Crossrefs

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), this sequence, A155061 (m=19), A155503 (m=20), A155676 (m=21), A155743 (m=22), A155829 (m=23), A155976 (m=24).

Programs

  • Magma
    SetDefaultRealField(RealField(100)); Log(18)/Log(9); // G. C. Greubel, Sep 01 2018
  • Mathematica
    RealDigits[Log[9, 18], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)
  • PARI
    default(realprecision, 100); log(18)/log(9) \\ G. C. Greubel, Sep 01 2018

Formula

Equals 1+A152747. - R. J. Mathar, Jan 07 2021
Equals A153495+1/2. - R. J. Mathar, Feb 15 2025

A155061 Decimal expansion of log_9 (19).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			1.3400719296231876724252833101095975652330714213471766109184...

Links

Crossrefs

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), A154947 (m=18), this sequence, A155503 (m=20), A155676 (m=21), A155743 (m=22), A155829 (m=23), A155976 (m=24).

Programs

  • Magma
    SetDefaultRealField(RealField(100)); Log(19)/Log(9); // G. C. Greubel, Sep 01 2018
  • Mathematica
    RealDigits[Log[9, 19], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)
  • PARI
    default(realprecision, 100); log(19)/log(9) \\ G. C. Greubel, Sep 01 2018

A155503 Decimal expansion of log_9 (20).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			1.3634165139304210206980473181820810524535518234649052723971...

Links

Crossrefs

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), A154947 (m=18), A155061 (m=19), this sequence, A155676 (m=21), A155743 (m=22), A155829 (m=23), A155976 (m=24).

Programs

  • Magma
    SetDefaultRealField(RealField(100)); Log(20)/Log(9); // G. C. Greubel, Sep 01 2018
  • Mathematica
    RealDigits[Log[9, 20], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)
  • PARI
    default(realprecision, 100); log(20)/log(9) \\ G. C. Greubel, Sep 01 2018

A155676 Decimal expansion of log_9 (21).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			1.3856218745807111300339641535412288590332356672971217396844...

Links

Crossrefs

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), A154947 (m=18), A155061 (m=19), A155503 (m=20), thus sequence, A155743 (m=22), A155829 (m=23), A155976 (m=24).

Programs

  • Magma
    SetDefaultRealField(RealField(100)); Log(21)/Log(9); // G. C. Greubel, Sep 01 2018
  • Mathematica
    RealDigits[Log[9,21],10,120][[1]] (* Harvey P. Dale, May 04 2012 *)
  • PARI
    default(realprecision, 100); log(21)/log(9) \\ G. C. Greubel, Sep 01 2018

A155743 Decimal expansion of log_9 (22).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			1.4067940461077977590742537645373448889212735826664123940539...

Links

Crossrefs

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), A154947 (m=18), A155061 (m=19), A155503 (m=20), A155676 (m=21), this sequence, A155829 (m=23), A155976 (m=24).

Programs

  • Magma
    SetDefaultRealField(RealField(100)); Log(22)/Log(9); // G. C. Greubel, Sep 01 2018
  • Mathematica
    RealDigits[Log[9, 22], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)
  • PARI
    default(realprecision, 100); log(22)/log(9) \\ G. C. Greubel, Sep 01 2018

A155829 Decimal expansion of log_9 (23).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			1.4270249151001355537018158824746039413815908185252448835867...

Links

Crossrefs

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), A154947 (m=18), A155061 (m=19), A155503 (m=20), A155676 (m=21), A155743 (m=22), this sequence, A155976 (m=24).

Programs

  • Magma
    SetDefaultRealField(RealField(100)); Log(23)/Log(9); // G. C. Greubel, Sep 01 2018
  • Mathematica
    RealDigits[Log[9, 23], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)
  • PARI
    default(realprecision, 100); log(23)/log(9) \\ G. C. Greubel, Sep 01 2018

A155976 Decimal expansion of log_9 (24).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			1.4463946303571861556492906715141412814493784601978206418059...

Links

Crossrefs

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), A154947 (m=18), A155061 (m=19), A155503 (m=20), A155676 (m=21), A155743 (m=22), A155829 (m=23), this sequence.

Programs

  • Magma
    SetDefaultRealField(RealField(100)); Log(24)/Log(9); // G. C. Greubel, Sep 01 2018
  • Mathematica
    RealDigits[Log[9, 24], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)
  • PARI
    default(realprecision, 100); log(24)/log(9) \\ G. C. Greubel, Sep 01 2018

A362843 Numbers that are equal to the sum of their digits raised to consecutive odd numbered powers (1,3,5,7,...).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 463, 3943, 371915027434113
Offset: 1

Views

Author

Wolfe Padawer, May 05 2023

Keywords

Comments

Unlike A032799 and A208130, this sequence is not easily proven to be finite. With m >= 1, 10^(m - 1) exceeds 9^1 + 9^2 + ... + 9^m when m is approximately 22.97, meaning it is impossible for an integer with 23 or more digits to be equal to the sum of its digits raised to the consecutive powers. However, 10^(m - 1) will never exceed 9^1 + 9^3 + ... + 9^(2m - 1) over m >= 1. It appears that 10^(m - 1) will never exceed 9^1 + 9^(1 + x) + 9^(1 + 2x) ... 9^(mx - x + 1) over m >= 1 when x >= A154160, approximately 1.04795. For A032799, x = 1, and for this sequence, x = 2. This means this sequence could theoretically be infinite, although it is currently unknown whether it is.
a(14) > 10^24 if it exists. The expected number of k-digit terms can be heuristically estimated as about 10^(-0.15*k), which suggests that the sequence is likely finite. - Max Alekseyev, May 17 2025

Examples

			1 = 1^1;
463 = 4^1 + 6^3 + 3^5;
3943 = 3^1 + 9^3 + 4^5 + 3^7.

Crossrefs

Cf. A032799, A154160, A208130.

Programs

  • Mathematica
    kmax=10^6; a={}; For[k=0, k<=kmax, k++,If[Sum[Part[IntegerDigits[k],i]^(2i-1),{i,IntegerLength[k]}]==k, AppendTo[a,k]]]; a (* Stefano Spezia, May 06 2023 *)
  • PARI
    isok(k) = my(d=digits(k)); sum(i=1, #d, d[i]^(2*i-1)) == k; \\ Michel Marcus, May 06 2023
  • Python
    from itertools import count, islice
def A362843_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:n==sum(int(d)**((i<<1)+1) for i,d in enumerate(str(n))),count(max(startvalue,0)))
A362843_list = list(islice(A362843_gen(),12)) # Chai Wah Wu, Jun 26 2023

Extensions

a(13) from Martin Ehrenstein, Jul 07 2023

A352735 Lucky numbers in Chinese: Numbers whose decimal expansion contains 8 but not 4.

Original entry on oeis.org

8, 18, 28, 38, 58, 68, 78, 80, 81, 82, 83, 85, 86, 87, 88, 89, 98, 108, 118, 128, 138, 158, 168, 178, 180, 181, 182, 183, 185, 186, 187, 188, 189, 198, 208, 218, 228, 238, 258, 268, 278, 280, 281, 282, 283, 285, 286, 287, 288, 289, 298, 308, 318, 328, 338, 358
Offset: 1

Views

Author

Charles R Greathouse IV, Mar 30 2022

Keywords

Comments

The number 8 (八) sounds like 发 = "to get rich". The number 4 (四) sounds like 死 = "to die". Many numbers are auspicious or inauspicious in Chinese numerology but these are perhaps the most common.

Crossrefs

Intersection of A052406 and A011538.

Programs

  • PARI
    is(n)=setintersect(Set(digits(n)),[4,8])==[8]

Formula

a(n) ≍ n^k where k = A154160 = 1.047951637....
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