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A309443 Coefficients in 5-adic expansion of 4^(1/3). 12
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 21 06:55 EDT 2021. Contains 345358 sequences. (Running on oeis4.)