A309445 Coefficients in 7-adic expansion of 2^(1/5).

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

Offset: 0

Author

Seiichi Manyama, Aug 03 2019

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A309450.

Digits of p-adic integers:

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

A309446 (7-adic, 3^(1/5));

A309447 (7-adic, 4^(1/5));

A309448 (7-adic, 5^(1/5));

A309449 (7-adic, 6^(1/5)).

Programs

Maple

op([1,3], padic:-rootp(x^5-2,7,101)); # Robert Israel, Aug 04 2019

PARI

Vecrev(digits(truncate((2+O(7^100))^(1/5)), 7))

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 A309445(n)
  A([-2, 0, 0, 0, 0, 1], 4, 7, n)
end
p A309445(100)