

A290567


The successive approximations up to 5^n for 5adic 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
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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(n1) + 2 * (a(n1)^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



