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.

Showing 1-4 of 4 results.

A018143 Powers of fifth root of 10 rounded up.

Original entry on oeis.org

1, 2, 3, 4, 7, 10, 16, 26, 40, 64, 100, 159, 252, 399, 631, 1000, 1585, 2512, 3982, 6310, 10000, 15849, 25119, 39811, 63096, 100000, 158490, 251189, 398108, 630958, 1000000, 1584894, 2511887, 3981072, 6309574
Offset: 0

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Crossrefs

Programs

  • Mathematica
    Ceiling[Surd[10,5]^Range[0,40]] (* Harvey P. Dale, Dec 30 2017 *)
  • PARI
    a(n) = sqrtnint(10^n-1, 5) + 1; \\ Michel Marcus, Jun 26 2024

A018141 Powers of fifth root of 10 rounded down.

Original entry on oeis.org

1, 1, 2, 3, 6, 10, 15, 25, 39, 63, 100, 158, 251, 398, 630, 1000, 1584, 2511, 3981, 6309, 10000, 15848, 25118, 39810, 63095, 100000, 158489, 251188, 398107, 630957, 1000000, 1584893, 2511886, 3981071, 6309573
Offset: 0

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Crossrefs

Programs

  • Mathematica
    Floor[(10^(1/5))^Range[0,40]] (* Harvey P. Dale, Sep 24 2012 *)
  • PARI
    a(n) = sqrtnint(10^n, 5); \\ Michel Marcus, Jun 26 2024

A018184 Powers of fifth root of 24 rounded to nearest integer.

Original entry on oeis.org

1, 2, 4, 7, 13, 24, 45, 86, 162, 305, 576, 1088, 2054, 3877, 7321, 13824, 26102, 49285, 93059, 175713, 331776, 626451, 1182849, 2233427, 4217101, 7962624, 15034828, 28388386, 53602242, 101210414, 191102976
Offset: 0

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Programs

  • Python
    from gmpy2 import iroot_rem
    def A018142(n):
        i,j = iroot_rem(24**n,5)
        return int(i) + int(32*j >= 10*i*(4*i*(2*i*(i + 1) + 1) + 1) + 1) # Chai Wah Wu, Aug 18 2016

A205770 Powers of fifth root of 100, rounded to the nearest integer.

Original entry on oeis.org

1, 3, 6, 16, 40, 100, 251, 631, 1585, 3981, 10000, 25119, 63096, 158489, 398107, 1000000, 2511886, 6309573, 15848932, 39810717, 100000000, 251188643, 630957344, 1584893192, 3981071706, 10000000000, 25118864315, 63095734448, 158489319246, 398107170553, 1000000000000
Offset: 0

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Comments

The fifth root of 100, known as Pogson's ratio, is the ratio between successive stellar magnitudes.

Crossrefs

Bisection of A018142, ratio is A189824.

Programs

  • Magma
    [Round(100^(n/5)): n in [0..30]]; // G. C. Greubel, Jan 14 2018
  • Mathematica
    Table[Round[100^(n/5)], {n, 0, 30}] (* G. C. Greubel, Jan 14 2018 *)
    Round[Surd[100,5]^Range[0,40]] (* Harvey P. Dale, Dec 03 2024 *)
  • PARI
    a(n)=round(100^(n/5)) \\ Charles R Greathouse IV, Jan 31 2012
    
  • Python
    from gmpy2 import iroot
    def A205770(n):
        m = 100**n
        i = iroot(m,5)[0]
        return int(i) + int(32*m >= (1+2*i)**5) # Chai Wah Wu, Aug 16 2016
    
Showing 1-4 of 4 results.