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

0,1

Links

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

Wikipedia, Hensel's Lemma.

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.

Prog

(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)

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.

Sequence in context: A166592 A103497 A191390 * A369997 A369605 A085747

Adjacent sequences: A309695 A309696 A309697 * A309699 A309700 A309701

Keyword

nonn,base

Author

Seiichi Manyama, Aug 13 2019

Status

approved