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 35 results. Next

A309569 Digits of the 10-adic integer (11/3)^(1/3).

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 10 2019

Keywords

Examples

			       3^3 == 7      (mod 10).
      33^3 == 37     (mod 10^2).
     233^3 == 337    (mod 10^3).
    2233^3 == 3337   (mod 10^4).
   52233^3 == 33337  (mod 10^5).
  852233^3 == 333337 (mod 10^6).

Links

Crossrefs

Cf. A173766, A309600, A309641.

Programs

  • PARI
    N=100; Vecrev(digits(lift(chinese(Mod((11/3+O(2^N))^(1/3), 2^N), Mod((11/3+O(5^N))^(1/3), 5^N)))), N)
  • Ruby
    def A309569(n)
  ary = [3]
  a = 3
  n.times{|i|
    b = (a + 9 * (3 * a ** 3 - 11)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309569(100)

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 3, b(n) = b(n-1) + 9 * (3 * b(n-1)^3 - 11) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

A309570 Digits of the 10-adic integer (17/3)^(1/3).

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 10 2019

Keywords

Examples

			       9^3 == 9      (mod 10).
      79^3 == 39     (mod 10^2).
     179^3 == 339    (mod 10^3).
    6179^3 == 3339   (mod 10^4).
   26179^3 == 33339  (mod 10^5).
  826179^3 == 333339 (mod 10^6).

Links

Crossrefs

Cf. A173764, A309600, A309640.

Programs

  • PARI
    N=100; Vecrev(digits(lift(chinese(Mod((17/3+O(2^N))^(1/3), 2^N), Mod((17/3+O(5^N))^(1/3), 5^N)))), N)
  • Ruby
    def A309570(n)
  ary = [9]
  a = 9
  n.times{|i|
    b = (a + 3 * a ** 3 - 17) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309570(100)

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 9, b(n) = b(n-1) + 3 * b(n-1)^3 - 17 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

A309595 Digits of the 10-adic integer (-31/9)^(1/3).

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 10 2019

Keywords

Examples

			       1^3 == 1      (mod 10).
      81^3 == 41     (mod 10^2).
      81^3 == 441    (mod 10^3).
    1081^3 == 4441   (mod 10^4).
   11081^3 == 44441  (mod 10^5).
  811081^3 == 444441 (mod 10^6).

Links

Crossrefs

Cf. A173768, A309600, A309614.

Programs

  • PARI
    N=100; Vecrev(digits(lift(chinese(Mod((-31/9+O(2^N))^(1/3), 2^N), Mod((-31/9+O(5^N))^(1/3), 5^N)))), N)
  • Ruby
    def A309595(n)
  ary = [1]
  a = 1
  n.times{|i|
    b = (a + 7 * (9 * a ** 3 + 31)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309595(100)

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 1, b(n) = b(n-1) + 7 * (9 * b(n-1)^3 + 31) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

A309601 Digits of the 10-adic integer (53/9)^(1/3).

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 09 2019

Keywords

Examples

			       3^3 == 7      (mod 10).
      73^3 == 17     (mod 10^2).
     373^3 == 117    (mod 10^3).
    8373^3 == 1117   (mod 10^4).
   68373^3 == 11117  (mod 10^5).
  768373^3 == 111117 (mod 10^6).

Links

Crossrefs

Cf. A309600.

Programs

  • PARI
    N=100; Vecrev(digits(lift(chinese(Mod((53/9+O(2^N))^(1/3), 2^N), Mod((53/9+O(5^N))^(1/3), 5^N)))), N)
  • Ruby
    def A309601(n)
  ary = [3]
  a = 3
  n.times{|i|
    b = (a + 3 * (9 * a ** 3 - 53)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309601(100)

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 3, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 - 53) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

A309602 Digits of the 10-adic integer (71/9)^(1/3).

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 09 2019

Keywords

Examples

			       9^3 == 9      (mod 10).
      39^3 == 19     (mod 10^2).
     639^3 == 119    (mod 10^3).
    8639^3 == 1119   (mod 10^4).
   38639^3 == 11119  (mod 10^5).
  238639^3 == 111119 (mod 10^6).

Links

Crossrefs

Cf. A165247, A309600, A309646.

Programs

  • PARI
    N=100; Vecrev(digits(lift(chinese(Mod((71/9+O(2^N))^(1/3), 2^N), Mod((71/9+O(5^N))^(1/3), 5^N)))), N)
  • Ruby
    def A309602(n)
  ary = [9]
  a = 9
  n.times{|i|
    b = (a + 7 * (9 * a ** 3 - 71)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309602(100)

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 9, b(n) = b(n-1) + 7 * (9 * b(n-1)^3 - 71) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

A309603 Digits of the 10-adic integer (-11/9)^(1/3).

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 09 2019

Keywords

Examples

			       1^3 == 1      (mod 10).
      41^3 == 21     (mod 10^2).
     141^3 == 221    (mod 10^3).
    3141^3 == 2221   (mod 10^4).
   33141^3 == 22221  (mod 10^5).
  433141^3 == 222221 (mod 10^6).

Links

Crossrefs

Cf. A165402, A309600, A309645.

Programs

  • PARI
    N=100; Vecrev(digits(lift(chinese(Mod((-11/9+O(2^N))^(1/3), 2^N), Mod((-11/9+O(5^N))^(1/3), 5^N)))), N)
  • Ruby
    def A309603(n)
  ary = [1]
  a = 1
  n.times{|i|
    b = (a + 7 * (9 * a ** 3 + 11)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309603(100)

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 1, b(n) = b(n-1) + 7 * (9 * b(n-1)^3 + 11) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

A309604 Digits of the 10-adic integer (43/9)^(1/3).

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 09 2019

Keywords

Examples

			      3^3 == 7      (mod 10).
      3^3 == 27     (mod 10^2).
    603^3 == 227    (mod 10^3).
   8603^3 == 2227   (mod 10^4).
  58603^3 == 22227  (mod 10^5).
  58603^3 == 222227 (mod 10^6).

Links

Crossrefs

Cf. A309600, A309644.

Programs

  • PARI
    N=100; Vecrev(digits(lift(chinese(Mod((43/9+O(2^N))^(1/3), 2^N), Mod((43/9+O(5^N))^(1/3), 5^N)))), N)
  • Ruby
    def A309604(n)
  ary = [3]
  a = 3
  n.times{|i|
    b = (a + 3 * (9 * a ** 3 - 43)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309604(100)

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 3, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 - 43) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

A309605 Digits of the 10-adic integer (61/9)^(1/3).

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 09 2019

Keywords

Examples

			       9^3 == 9      (mod 10).
       9^3 == 29     (mod 10^2).
     509^3 == 229    (mod 10^3).
     509^3 == 2229   (mod 10^4).
   50509^3 == 22229  (mod 10^5).
  450509^3 == 222229 (mod 10^6).

Links

Crossrefs

Cf. A309600, A309643.

Programs

  • PARI
    N=100; Vecrev(digits(lift(chinese(Mod((61/9+O(2^N))^(1/3), 2^N), Mod((61/9+O(5^N))^(1/3), 5^N)))), N)
  • Ruby
    def A309605(n)
  ary = [9]
  a = 9
  n.times{|i|
    b = (a + 7 * (9 * a ** 3 - 61)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309605(100)

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 9, b(n) = b(n-1) + 7 * (9 * b(n-1)^3 - 61) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

A309606 Digits of the 10-adic integer (-7/3)^(1/3).

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 09 2019

Keywords

Examples

			       1^3 == 1      (mod 10).
      11^3 == 31     (mod 10^2).
      11^3 == 331    (mod 10^3).
    4011^3 == 3331   (mod 10^4).
   64011^3 == 33331  (mod 10^5).
  764011^3 == 333331 (mod 10^6).

Links

Crossrefs

Cf. A309600, A309642.

Programs

  • Maple
    op([1,3],padic:-rootp(x^3+7/3,10,100)); # Robert Israel, Aug 09 2019
  • PARI
    N=100; Vecrev(digits(lift(chinese(Mod((-7/3+O(2^N))^(1/3), 2^N), Mod((-7/3+O(5^N))^(1/3), 5^N)))), N)
  • Ruby
    def A309606(n)
  ary = [1]
  a = 1
  n.times{|i|
    b = (a + 3 * a ** 3 + 7) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309606(100)

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 1, b(n) = b(n-1) + 3 * b(n-1)^3 + 7 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

A309608 Digits of the 10-adic integer (-13/9)^(1/3).

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 10 2019

Keywords

Examples

			       7^3 == 3      (mod 10).
       7^3 == 43     (mod 10^2).
     307^3 == 443    (mod 10^3).
     307^3 == 4443   (mod 10^4).
   30307^3 == 44443  (mod 10^5).
  330307^3 == 444443 (mod 10^6).

Links

Crossrefs

Cf. A173770, A309600, A309613.

Programs

  • PARI
    N=100; Vecrev(digits(lift(chinese(Mod((-13/9+O(2^N))^(1/3), 2^N), Mod((-13/9+O(5^N))^(1/3), 5^N)))), N)
  • Ruby
    def A309608(n)
  ary = [7]
  a = 7
  n.times{|i|
    b = (a + 3 * (9 * a ** 3 + 13)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309608(100)

Formula

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 + 13) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
Previous Showing 11-20 of 35 results. Next

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