A322931 -id:A322931 - cp's OEIS frontend

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

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

Seiichi Manyama, Aug 13 2019

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Wikipedia, Hensel's Lemma.

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.

N=100; Vecrev(digits(lift((3+O(2^(2*N)))^(1/3)), 4), N)

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)

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.

A322932 Digits of the 8-adic integer 5^(1/3).

Original entry on oeis.org

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

Offset: 0

Patrick A. Thomas, Dec 31 2018

			20447135^3 == 5 (mod 8^8) in octal.

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Wikipedia, Hensel's Lemma.

Cf. A322931, A322933.

N=100; Vecrev(digits(lift((5+O(2^(3*N)))^(1/3)), 8), N) \\ Seiichi Manyama, Aug 14 2019

def A322932(n)
  ary = [5]
  a = 5
  n.times{|i|
    b = (a + 5 * (a ** 3 - 5)) % (8 ** (i + 2))
    ary << (b - a) / (8 ** (i + 1))
    a = b
  }
  ary
end
p A322932(100) # Seiichi Manyama, Aug 14 2019

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 5, b(n) = b(n-1) + 5 * (b(n-1)^3 - 5) mod 8^n for n > 1, then a(n) = (b(n+1) - b(n))/8^n. - Seiichi Manyama, Aug 14 2019

A322933 Digits of the 8-adic integer 7^(1/3).

Original entry on oeis.org

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

Offset: 0

Patrick A. Thomas, Dec 31 2018

The octal version of A225405.

			56027726627^3 == 7 (mod 8^11) in octal.

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Wikipedia, Hensel's Lemma.

Cf. A225405 (decimal version), A322931, A322932.

N=100; Vecrev(digits(lift((7+O(2^(3*N)))^(1/3)), 8), N) \\ Seiichi Manyama, Aug 14 2019

def A322933(n)
  ary = [7]
  a = 7
  n.times{|i|
    b = (a + 5 * (a ** 3 - 7)) % (8 ** (i + 2))
    ary << (b - a) / (8 ** (i + 1))
    a = b
  }
  ary
end
p A322933(100) # Seiichi Manyama, Aug 14 2019

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + 5 * (b(n-1)^3 - 7) mod 8^n for n > 1, then a(n) = (b(n+1) - b(n))/8^n. - Seiichi Manyama, Aug 14 2019

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

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A322932 Digits of the 8-adic integer 5^(1/3).

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A322933 Digits of the 8-adic integer 7^(1/3).

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