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A290567 The successive approximations up to 5^n for 5-adic integer 2^(1/3). 17
0, 3, 3, 53, 303, 2178, 5303, 67803, 67803, 849053, 6708428, 6708428, 6708428, 983270928, 983270928, 25397333428, 147467645928, 605231317803, 1368170770928, 5182868036553, 43329840692803, 43329840692803, 43329840692803, 4811701422724053, 52495417243036553 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

x   = ...132203,

x^2 = ...344214,

x^3 = ...000002 = 2.

LINKS

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

Wikipedia, Hensel's Lemma.

FORMULA

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

EXAMPLE

a(1) = (   3)_5 = 3,

a(2) = (   3)_5 = 3,

a(3) = ( 203)_5 = 53,

a(4) = (2203)_5 = 303.

PROG

(PARI) a(n)=truncate((2+O(5^n))^(1/3)); \\ Joerg Arndt, Aug 06 2017

CROSSREFS

Cf. A290566, A290568.

Sequence in context: A292753 A268136 A225208 * A100065 A066807 A165497

Adjacent sequences:  A290564 A290565 A290566 * A290568 A290569 A290570

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 06 2017

STATUS

approved

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Last modified January 23 10:48 EST 2020. Contains 331171 sequences. (Running on oeis4.)