A309443 Coefficients in 5-adic expansion of 4^(1/3).

4, 1, 2, 4, 4, 3, 3, 4, 0, 4, 2, 1, 1, 1, 4, 2, 2, 3, 3, 2, 3, 4, 2, 3, 2, 0, 3, 4, 2, 1, 4, 3, 3, 3, 4, 4, 0, 3, 2, 0, 0, 2, 4, 2, 3, 4, 4, 1, 4, 4, 1, 3, 1, 2, 2, 0, 3, 0, 1, 1, 3, 2, 0, 0, 0, 1, 2, 1, 4, 2, 1, 0, 4, 0, 2, 1, 4, 0, 0, 3, 1, 0, 4, 1, 2, 4, 2, 0, 1, 4, 4

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Maple

op([1, 3], padic:-rootp(x^3-4, 5, 101)); # Robert Israel, Aug 04 2019

Prog

(Ruby)
require 'OpenSSL'
def f_a(ary, a)
  (0..ary.size - 1).inject(0){|s, i| s + ary[i] * a ** i}
end
def df(ary)
  (1..ary.size - 1).map{|i| i * ary[i]}
end
def A(c_ary, k, m, n)
  x = OpenSSL::BN.new((-f_a(df(c_ary), k)).to_s).mod_inverse(m).to_i % m
  f_ary = c_ary.map{|i| x * i}
  f_ary[1] += 1
  d_ary = []
  ary = [0]
  a, mod = k, m
  (n + 1).times{|i|
    b = a % mod
    d_ary << (b - ary[-1]) / m ** i
    ary << b
    a = f_a(f_ary, b)
    mod *= m
  }
  d_ary
end
def A309443(n)
  A([-4, 0, 0, 1], 4, 5, n)
end
p A309443(100)
(PARI) Vecrev(digits(truncate((4+O(5^100))^(1/3)), 5))

Crossrefs

Cf. A309444.

Digits of p-adic integers:

A269591, A269592 (5-adic, sqrt(-4));

A210850, A210851 (5-adic, sqrt(-1));

A290566 (5-adic, 2^(1/3));

A290563 (5-adic, 3^(1/3)).

Sequence in context: A010126 A021712 A307550 * A014571 A327320 A324466

Adjacent sequences: A309440 A309441 A309442 * A309444 A309445 A309446

Keyword

nonn,base

Author

Seiichi Manyama, Aug 03 2019

Status

approved