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A290568 The successive approximations up to 5^n for 5-adic integer 3^(1/3). 17

%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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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)