cp's OEIS Frontend

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

%I A309445 #13 Aug 04 2019 01:38:29
%S A309445 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,
%T A309445 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,
%U A309445 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
%N A309445 Coefficients in 7-adic expansion of 2^(1/5).
%H A309445 Robert Israel, <a href="/A309445/b309445.txt">Table of n, a(n) for n = 0..10000</a>
%p A309445 op([1,3], padic:-rootp(x^5-2,7,101)); # _Robert Israel_, Aug 04 2019
%o A309445 (Ruby)
%o A309445 require 'OpenSSL'
%o A309445 def f_a(ary, a)
%o A309445   (0..ary.size - 1).inject(0){|s, i| s + ary[i] * a ** i}
%o A309445 end
%o A309445 def df(ary)
%o A309445   (1..ary.size - 1).map{|i| i * ary[i]}
%o A309445 end
%o A309445 def A(c_ary, k, m, n)
%o A309445   x = OpenSSL::BN.new((-f_a(df(c_ary), k)).to_s).mod_inverse(m).to_i % m
%o A309445   f_ary = c_ary.map{|i| x * i}
%o A309445   f_ary[1] += 1
%o A309445   d_ary = []
%o A309445   ary = [0]
%o A309445   a, mod = k, m
%o A309445   (n + 1).times{|i|
%o A309445     b = a % mod
%o A309445     d_ary << (b - ary[-1]) / m ** i
%o A309445     ary << b
%o A309445     a = f_a(f_ary, b)
%o A309445     mod *= m
%o A309445   }
%o A309445   d_ary
%o A309445 end
%o A309445 def A309445(n)
%o A309445   A([-2, 0, 0, 0, 0, 1], 4, 7, n)
%o A309445 end
%o A309445 p A309445(100)
%o A309445 (PARI) Vecrev(digits(truncate((2+O(7^100))^(1/5)), 7))
%Y A309445 Cf. A309450.
%Y A309445 Digits of p-adic integers:
%Y A309445 A290566 (5-adic, 2^(1/3));
%Y A309445 A309446 (7-adic, 3^(1/5));
%Y A309445 A309447 (7-adic, 4^(1/5));
%Y A309445 A309448 (7-adic, 5^(1/5));
%Y A309445 A309449 (7-adic, 6^(1/5)).
%K A309445 nonn,base
%O A309445 0,1
%A A309445 _Seiichi Manyama_, Aug 03 2019