A309443 - OEIS

%I #19 Aug 04 2019 01:38:26

%S 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,

%T 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,

%U 4,2,1,0,4,0,2,1,4,0,0,3,1,0,4,1,2,4,2,0,1,4,4

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

%H Robert Israel, <a href="/A309443/b309443.txt">Table of n, a(n) for n = 0..10000</a>

%p op([1,3], padic:-rootp(x^3-4,5,101)); # _Robert Israel_, Aug 04 2019

%o (Ruby)

%o require 'OpenSSL'

%o def f_a(ary, a)

%o   (0..ary.size - 1).inject(0){|s, i| s + ary[i] * a ** i}

%o end

%o def df(ary)

%o   (1..ary.size - 1).map{|i| i * ary[i]}

%o end

%o def A(c_ary, k, m, n)

%o   x = OpenSSL::BN.new((-f_a(df(c_ary), k)).to_s).mod_inverse(m).to_i % m

%o   f_ary = c_ary.map{|i| x * i}

%o   f_ary[1] += 1

%o   d_ary = []

%o   ary = [0]

%o   a, mod = k, m

%o   (n + 1).times{|i|

%o     b = a % mod

%o     d_ary << (b - ary[-1]) / m ** i

%o     ary << b

%o     a = f_a(f_ary, b)

%o     mod *= m

%o   }

%o   d_ary

%o end

%o def A309443(n)

%o   A([-4, 0, 0, 1], 4, 5, n)

%o end

%o p A309443(100)

%o (PARI) Vecrev(digits(truncate((4+O(5^100))^(1/3)), 5))

%Y Cf. A309444.

%Y Digits of p-adic integers:

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

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

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

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

%K nonn,base

%O 0,1

%A _Seiichi Manyama_, Aug 03 2019