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A290568
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The successive approximations up to 5^n for 5-adic integer 3^(1/3).
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17
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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
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OFFSET
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0,2
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COMMENTS
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x = ...301322,
x^2 = ...114234,
x^3 = ...000003 = 3.
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LINKS
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FORMULA
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a(0) = 0 and a(1) = 2, a(n) = a(n-1) + 2 * (a(n-1)^3 - 3) mod 5^n for n > 1.
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EXAMPLE
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a(1) = ( 2)_5 = 2,
a(2) = ( 22)_5 = 12,
a(3) = ( 322)_5 = 87,
a(4) = (1322)_5 = 212.
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PROG
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(PARI) a(n)=truncate((3+O(5^n))^(1/3)); \\ Joerg Arndt, Aug 06 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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