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A309723 Digits of the 6-adic integer (1/5)^(1/5).

%I A309723 #16 Aug 17 2019 05:06:43
%S A309723 5,0,4,5,5,1,5,4,1,2,0,3,5,3,2,5,0,0,5,4,5,3,0,3,4,2,0,0,1,4,0,0,1,2,
%T A309723 2,3,3,4,5,4,4,5,3,1,1,5,2,0,5,4,2,2,5,4,0,2,5,5,4,2,1,1,4,2,2,4,5,4,
%U A309723 1,5,0,1,0,4,2,1,3,4,0,1,2,0,0,3,3,1,3,4,2,3,4,2,5,0,3,3,0,1,2,0,4
%N A309723 Digits of the 6-adic integer (1/5)^(1/5).
%H A309723 Seiichi Manyama, <a href="/A309723/b309723.txt">Table of n, a(n) for n = 0..10000</a>
%H A309723 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hensel%27s_lemma">Hensel's Lemma</a>.
%F A309723 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 5, b(n) = b(n-1) + 5 * (5 * b(n-1)^5 - 1) mod 6^n for n > 1, then a(n) = (b(n+1) - b(n))/6^n.
%o A309723 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((1/5+O(2^N))^(1/5), 2^N), Mod((1/5+O(3^N))^(1/5), 3^N))), 6), N)
%o A309723 (Ruby)
%o A309723 def A309723(n)
%o A309723   ary = [5]
%o A309723   a = 5
%o A309723   n.times{|i|
%o A309723     b = (a + 5 * (5 * a ** 5 - 1)) % (6 ** (i + 2))
%o A309723     ary << (b - a) / (6 ** (i + 1))
%o A309723     a = b
%o A309723   }
%o A309723   ary
%o A309723 end
%o A309723 p A309723(100)
%Y A309723 Digits of the k-adic integer (1/(k-1))^(1/(k-1)): A309722 (k=4), this sequence (k=6), A309724 (k=8), A225464 (k=10).
%Y A309723 Cf. A309699.
%K A309723 nonn,base
%O A309723 0,1
%A A309723 _Seiichi Manyama_, Aug 14 2019