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

0, 2, 12, 87, 212, 212, 9587, 56462, 212712, 603337, 4509587, 4509587, 4509587, 4509587, 2445915837, 20756462712, 142826775212, 600590447087, 2889408806462, 18148197868962, 94442143181462, 94442143181462, 1524953617790837, 6293325199822087, 6293325199822087, 125502614750603337

Offset: 0

Author

Seiichi Manyama, Aug 06 2017

Keywords

• nonn

Comments

x = ...301322,

x^2 = ...114234,

x^3 = ...000003 = 3.

Examples

			a(1) = (   2)_5 = 2,
a(2) = (  22)_5 = 12,
a(3) = ( 322)_5 = 87,
a(4) = (1322)_5 = 212.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1431
• Wikipedia, Hensel's Lemma.

Crossrefs

Cf. A290563, A290567.

Programs

PARI

a(n)=truncate((3+O(5^n))^(1/3)); \\ Joerg Arndt, Aug 06 2017

Formula

a(0) = 0 and a(1) = 2, a(n) = a(n-1) + 2 * (a(n-1)^3 - 3) mod 5^n for n > 1.