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

%I A309443 #19 Aug 04 2019 01:38:26
%S A309443 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 A309443 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 A309443 4,2,1,0,4,0,2,1,4,0,0,3,1,0,4,1,2,4,2,0,1,4,4
%N A309443 Coefficients in 5-adic expansion of 4^(1/3).
%H A309443 Robert Israel, <a href="/A309443/b309443.txt">Table of n, a(n) for n = 0..10000</a>
%p A309443 op([1,3], padic:-rootp(x^3-4,5,101)); # _Robert Israel_, Aug 04 2019
%o A309443 (Ruby)
%o A309443 require 'OpenSSL'
%o A309443 def f_a(ary, a)
%o A309443   (0..ary.size - 1).inject(0){|s, i| s + ary[i] * a ** i}
%o A309443 end
%o A309443 def df(ary)
%o A309443   (1..ary.size - 1).map{|i| i * ary[i]}
%o A309443 end
%o A309443 def A(c_ary, k, m, n)
%o A309443   x = OpenSSL::BN.new((-f_a(df(c_ary), k)).to_s).mod_inverse(m).to_i % m
%o A309443   f_ary = c_ary.map{|i| x * i}
%o A309443   f_ary[1] += 1
%o A309443   d_ary = []
%o A309443   ary = [0]
%o A309443   a, mod = k, m
%o A309443   (n + 1).times{|i|
%o A309443     b = a % mod
%o A309443     d_ary << (b - ary[-1]) / m ** i
%o A309443     ary << b
%o A309443     a = f_a(f_ary, b)
%o A309443     mod *= m
%o A309443   }
%o A309443   d_ary
%o A309443 end
%o A309443 def A309443(n)
%o A309443   A([-4, 0, 0, 1], 4, 5, n)
%o A309443 end
%o A309443 p A309443(100)
%o A309443 (PARI) Vecrev(digits(truncate((4+O(5^100))^(1/3)), 5))
%Y A309443 Cf. A309444.
%Y A309443 Digits of p-adic integers:
%Y A309443 A269591, A269592 (5-adic, sqrt(-4));
%Y A309443 A210850, A210851 (5-adic, sqrt(-1));
%Y A309443 A290566 (5-adic, 2^(1/3));
%Y A309443 A290563 (5-adic, 3^(1/3)).
%K A309443 nonn,base
%O A309443 0,1
%A A309443 _Seiichi Manyama_, Aug 03 2019