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A290568 The successive approximations up to 5^n for 5-adic integer 3^(1/3). 17
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

x   = ...301322,

x^2 = ...114234,

x^3 = ...000003 = 3.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1431

Wikipedia, Hensel's Lemma.

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.

EXAMPLE

a(1) = (   2)_5 = 2,

a(2) = (  22)_5 = 12,

a(3) = ( 322)_5 = 87,

a(4) = (1322)_5 = 212.

PROG

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

CROSSREFS

Cf. A290563, A290567.

Sequence in context: A097237 A055531 A305209 * A181345 A193125 A305868

Adjacent sequences:  A290565 A290566 A290567 * A290569 A290570 A290571

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 06 2017

STATUS

approved

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)