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 1-5 of 5 results.

A309448 Coefficients in 7-adic expansion of 5^(1/5).

Original entry on oeis.org

3, 6, 6, 3, 3, 2, 5, 5, 4, 0, 6, 6, 2, 2, 3, 6, 6, 3, 1, 3, 2, 4, 4, 0, 4, 1, 5, 1, 2, 2, 2, 2, 6, 1, 0, 5, 6, 1, 3, 0, 3, 2, 6, 2, 5, 6, 6, 4, 6, 3, 0, 6, 6, 1, 6, 0, 0, 2, 5, 5, 4, 1, 3, 0, 0, 0, 4, 3, 2, 4, 0, 1, 4, 2, 0, 4, 5, 4, 1, 0, 0, 6, 5, 3, 1, 4, 2, 2, 6, 6, 2, 5, 2
Offset: 0

Views

Author

Seiichi Manyama, Aug 03 2019

Keywords

Links

Crossrefs

Cf. A309453.
Digits of p-adic integers:
A309699 (6-adic, 5^(1/5));
A309445 (7-adic, 2^(1/5));
A309446 (7-adic, 3^(1/5));
A309447 (7-adic, 4^(1/5));
A309449 (7-adic, 6^(1/5)).

Programs

  • PARI
    Vecrev(digits(truncate((5+O(7^100))^(1/5)), 7))

A309698 Digits of the 4-adic integer 3^(1/3).

Original entry on oeis.org

3, 2, 3, 1, 1, 0, 3, 3, 1, 0, 2, 0, 3, 3, 0, 3, 1, 3, 0, 1, 1, 3, 0, 3, 3, 3, 3, 3, 1, 0, 3, 2, 0, 2, 0, 0, 1, 2, 3, 2, 0, 3, 1, 0, 1, 1, 1, 2, 1, 2, 0, 1, 0, 1, 3, 2, 2, 1, 1, 1, 3, 2, 2, 0, 3, 3, 3, 0, 3, 0, 0, 0, 3, 0, 2, 3, 3, 0, 3, 2, 1, 2, 1, 2, 2, 1, 0, 0, 0, 2, 0, 1, 3, 0
Offset: 0

Views

Author

Seiichi Manyama, Aug 13 2019

Keywords

Links

Crossrefs

Digits of the k-adic integer (k-1)^(1/(k-1)): this sequence (k=4), A309699 (k=6), A309700 (k=8), A225458 (k=10).
Cf. A225404, A290563, A322931.

Programs

  • PARI
    N=100; Vecrev(digits(lift((3+O(2^(2*N)))^(1/3)), 4), N)
  • Ruby
    def A309698(n)
  ary = [3]
  a = 3
  n.times{|i|
    b = (a + a ** 3 - 3) % (4 ** (i + 2))
    ary << (b - a) / (4 ** (i + 1))
    a = b
  }
  ary
end
p A309698(100)

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 3, b(n) = b(n-1) + b(n-1)^3 - 3 mod 4^n for n > 1, then a(n) = (b(n+1) - b(n))/4^n.

A225458 10-adic integer x such that x^9 = 9.

Original entry on oeis.org

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

Views

Author

Aswini Vaidyanathan, May 11 2013

Keywords

Examples

			       9^9 == 9 (mod 10).
      89^9 == 9 (mod 10^2).
     289^9 == 9 (mod 10^3).
    1289^9 == 9 (mod 10^4).
   21289^9 == 9 (mod 10^5).
  921289^9 == 9 (mod 10^6).

Links

Crossrefs

Digits of the k-adic integer (k-1)^(1/(k-1)): A309698 (k=4), A309699 (k=6), A309700 (k=8), this sequence (k=10).

Programs

  • PARI
    n=0;for(i=1,100,m=9;for(x=0,9,if(((n+(x*10^(i-1)))^9)%(10^i)==m,n=n+(x*10^(i-1));print1(x", ");break)))
  • PARI
    N=100; Vecrev(digits(lift(chinese(Mod((9+O(2^N))^(1/9), 2^N), Mod((9+O(5^N))^(1/9), 5^N)))), N) \\ Seiichi Manyama, Aug 06 2019
  • Ruby
    def A225458(n)
  ary = [9]
  a = 9
  n.times{|i|
    b = (a + a ** 9 - 9) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A225458(100) # Seiichi Manyama, Aug 14 2019

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 9, b(n) = b(n-1) + b(n-1)^9 - 9 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n. - Seiichi Manyama, Aug 14 2019

A309700 Digits of the 8-adic integer 7^(1/7).

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 13 2019

Keywords

Links

Crossrefs

Digits of the k-adic integer (k-1)^(1/(k-1)): A309698 (k=4), A309699 (k=6), this sequence (k=8), A225458 (k=10).
Cf. A225445.

Programs

  • PARI
    N=100; Vecrev(digits(lift((7+O(2^(3*N)))^(1/7)), 8), N)
  • Ruby
    def A309700(n)
  ary = [7]
  a = 7
  n.times{|i|
    b = (a + a ** 7 - 7) % (8 ** (i + 2))
    ary << (b - a) / (8 ** (i + 1))
    a = b
  }
  ary
end
p A309700(100)

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + b(n-1)^7 - 7 mod 8^n for n > 1, then a(n) = (b(n+1) - b(n))/8^n.

A309723 Digits of the 6-adic integer (1/5)^(1/5).

Original entry on oeis.org

5, 0, 4, 5, 5, 1, 5, 4, 1, 2, 0, 3, 5, 3, 2, 5, 0, 0, 5, 4, 5, 3, 0, 3, 4, 2, 0, 0, 1, 4, 0, 0, 1, 2, 2, 3, 3, 4, 5, 4, 4, 5, 3, 1, 1, 5, 2, 0, 5, 4, 2, 2, 5, 4, 0, 2, 5, 5, 4, 2, 1, 1, 4, 2, 2, 4, 5, 4, 1, 5, 0, 1, 0, 4, 2, 1, 3, 4, 0, 1, 2, 0, 0, 3, 3, 1, 3, 4, 2, 3, 4, 2, 5, 0, 3, 3, 0, 1, 2, 0, 4
Offset: 0

Views

Author

Seiichi Manyama, Aug 14 2019

Keywords

Links

Crossrefs

Digits of the k-adic integer (1/(k-1))^(1/(k-1)): A309722 (k=4), this sequence (k=6), A309724 (k=8), A225464 (k=10).
Cf. A309699.

Programs

  • PARI
    N=100; Vecrev(digits(lift(chinese(Mod((1/5+O(2^N))^(1/5), 2^N), Mod((1/5+O(3^N))^(1/5), 3^N))), 6), N)
  • Ruby
    def A309723(n)
  ary = [5]
  a = 5
  n.times{|i|
    b = (a + 5 * (5 * a ** 5 - 1)) % (6 ** (i + 2))
    ary << (b - a) / (6 ** (i + 1))
    a = b
  }
  ary
end
p A309723(100)

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 5, b(n) = b(n-1) + 5 * (5 * b(n-1)^5 - 1) mod 6^n for n > 1, then a(n) = (b(n+1) - b(n))/6^n.
Showing 1-5 of 5 results.

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