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%I #16 Aug 07 2017 09:12:07
%S 0,2,12,87,212,212,9587,56462,212712,603337,4509587,4509587,4509587,
%T 4509587,2445915837,20756462712,142826775212,600590447087,
%U 2889408806462,18148197868962,94442143181462,94442143181462,1524953617790837,6293325199822087,6293325199822087,125502614750603337
%N The successive approximations up to 5^n for 5-adic integer 3^(1/3).
%C x = ...301322,
%C x^2 = ...114234,
%C x^3 = ...000003 = 3.
%H Seiichi Manyama, <a href="/A290568/b290568.txt">Table of n, a(n) for n = 0..1431</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hensel%27s_lemma">Hensel's Lemma</a>.
%F a(0) = 0 and a(1) = 2, a(n) = a(n-1) + 2 * (a(n-1)^3 - 3) mod 5^n for n > 1.
%e a(1) = ( 2)_5 = 2,
%e a(2) = ( 22)_5 = 12,
%e a(3) = ( 322)_5 = 87,
%e a(4) = (1322)_5 = 212.
%o (PARI) a(n)=truncate((3+O(5^n))^(1/3)); \\ _Joerg Arndt_, Aug 06 2017
%Y Cf. A290563, A290567.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Aug 06 2017
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