A309600 -id:A309600 - cp's OEIS frontend

A309609 Digits of the 10-adic integer (23/9)^(1/3).

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

Offset: 0

Seiichi Manyama, Aug 10 2019

			       3^3 == 7      (mod 10).
      63^3 == 47     (mod 10^2).
     263^3 == 447    (mod 10^3).
    9263^3 == 4447   (mod 10^4).
   79263^3 == 44447  (mod 10^5).
  679263^3 == 444447 (mod 10^6).

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A173772, A309600, A309612.

N=100; Vecrev(digits(lift(chinese(Mod((23/9+O(2^N))^(1/3), 2^N), Mod((23/9+O(5^N))^(1/3), 5^N)))), N)

def A309609(n)
  ary = [3]
  a = 3
  n.times{|i|
    b = (a + 3 * (9 * a ** 3 - 23)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309609(100)

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 - 23) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n

A309610 Digits of the 10-adic integer (41/9)^(1/3).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Aug 10 2019

			       9^3 == 9      (mod 10).
      49^3 == 49     (mod 10^2).
     649^3 == 449    (mod 10^3).
    5649^3 == 4449   (mod 10^4).
   95649^3 == 44449  (mod 10^5).
  695649^3 == 444449 (mod 10^6).

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A173776, A309600, A309611.

N=100; Vecrev(digits(lift(chinese(Mod((41/9+O(2^N))^(1/3), 2^N), Mod((41/9+O(5^N))^(1/3), 5^N)))), N)

def A309610(n)
  ary = [9]
  a = 9
  n.times{|i|
    b = (a + 7 * (9 * a ** 3 - 41)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309610(100)

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 - 41) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n

A309611 Digits of the 10-adic integer (-41/9)^(1/3).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Aug 10 2019

			       1^3 == 1      (mod 10).
      51^3 == 51     (mod 10^2).
     351^3 == 551    (mod 10^3).
    4351^3 == 5551   (mod 10^4).
    4351^3 == 55551  (mod 10^5).
  304351^3 == 555551 (mod 10^6).

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A173804, A309600, A309610.

N=100; Vecrev(digits(lift(chinese(Mod((-41/9+O(2^N))^(1/3), 2^N), Mod((-41/9+O(5^N))^(1/3), 5^N)))), N)

def A309611(n)
  ary = [1]
  a = 1
  n.times{|i|
    b = (a + 7 * (9 * a ** 3 + 41)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309611(100)

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 + 41) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n

A309612 Digits of the 10-adic integer (-23/9)^(1/3).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Aug 10 2019

			       7^3 == 3      (mod 10).
      37^3 == 53     (mod 10^2).
     737^3 == 553    (mod 10^3).
     737^3 == 5553   (mod 10^4).
   20737^3 == 55553  (mod 10^5).
  320737^3 == 555553 (mod 10^6).

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A173802, A309600, A309609.

N=100; Vecrev(digits(lift(chinese(Mod((-23/9+O(2^N))^(1/3), 2^N), Mod((-23/9+O(5^N))^(1/3), 5^N)))), N)

def A309612(n)
  ary = [7]
  a = 7
  n.times{|i|
    b = (a + 3 * (9 * a ** 3 + 23)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309612(100)

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 + 23) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n

A309613 Digits of the 10-adic integer (13/9)^(1/3).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Aug 10 2019

			       3^3 == 7      (mod 10).
      93^3 == 57     (mod 10^2).
     693^3 == 557    (mod 10^3).
    9693^3 == 5557   (mod 10^4).
   69693^3 == 55557  (mod 10^5).
  669693^3 == 555557 (mod 10^6).

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A178769, A309600, A309608.

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)

def A309613(n)
  ary = [3]
  a = 3
  n.times{|i|
    b = (a + 3 * (9 * a ** 3 - 13)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309613(100)

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 - 13) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

A309614 Digits of the 10-adic integer (31/9)^(1/3).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Aug 10 2019

			       9^3 == 9      (mod 10).
      19^3 == 59     (mod 10^2).
     919^3 == 559    (mod 10^3).
    8919^3 == 5559   (mod 10^4).
   88919^3 == 55559  (mod 10^5).
  188919^3 == 555559 (mod 10^6).

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A309595, A309600.

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)

def A309614(n)
  ary = [9]
  a = 9
  n.times{|i|
    b = (a + 7 * (9 * a ** 3 - 31)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309614(100)

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 - 31) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

A309640 Digits of the 10-adic integer (-17/3)^(1/3).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Aug 11 2019

			       1^3 == 1      (mod 10).
      21^3 == 61     (mod 10^2).
     821^3 == 661    (mod 10^3).
    3821^3 == 6661   (mod 10^4).
   73821^3 == 66661  (mod 10^5).
  173821^3 == 666661 (mod 10^6).

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A309570, A309600.

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)

def A309640(n)
  ary = [1]
  a = 1
  n.times{|i|
    b = (a + 3 * a ** 3 + 17) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309640(100)

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 + 17 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

A309641 Digits of the 10-adic integer (-11/3)^(1/3).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Aug 11 2019

			       7^3 == 3      (mod 10).
      67^3 == 63     (mod 10^2).
     767^3 == 663    (mod 10^3).
    7767^3 == 6663   (mod 10^4).
   47767^3 == 66663  (mod 10^5).
  147767^3 == 666663 (mod 10^6).

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A309569, A309600.

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)

def A309641(n)
  ary = [7]
  a = 7
  n.times{|i|
    b = (a + 9 * (3 * a ** 3 + 11)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309641(100)

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, 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.

A309642 Digits of the 10-adic integer (7/3)^(1/3).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Aug 11 2019

nonn

			       9^3 == 9      (mod 10).
      89^3 == 69     (mod 10^2).
     989^3 == 669    (mod 10^3).
    5989^3 == 6669   (mod 10^4).
   35989^3 == 66669  (mod 10^5).
  235989^3 == 666669 (mod 10^6).

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A309600, A309606.

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)

def A309642(n)
  ary = [9]
  a = 9
  n.times{|i|
    b = (a + 3 * a ** 3 - 7) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309642(100)

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 - 7 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

A309643 Digits of the 10-adic integer (-61/9)^(1/3).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Aug 11 2019

			       1^3 == 1      (mod 10).
      91^3 == 71     (mod 10^2).
     491^3 == 771    (mod 10^3).
    9491^3 == 7771   (mod 10^4).
   49491^3 == 77771  (mod 10^5).
  549491^3 == 777771 (mod 10^6).

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A309600, A309605.

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)

def A309643(n)
  ary = [1]
  a = 1
  n.times{|i|
    b = (a + 7 * (9 * a ** 3 + 61)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309643(100)

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 + 61) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

cp's OEIS Frontend

A309609 Digits of the 10-adic integer (23/9)^(1/3).

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A309610 Digits of the 10-adic integer (41/9)^(1/3).

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A309611 Digits of the 10-adic integer (-41/9)^(1/3).

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A309612 Digits of the 10-adic integer (-23/9)^(1/3).

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A309613 Digits of the 10-adic integer (13/9)^(1/3).

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A309614 Digits of the 10-adic integer (31/9)^(1/3).

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A309640 Digits of the 10-adic integer (-17/3)^(1/3).

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A309641 Digits of the 10-adic integer (-11/3)^(1/3).

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