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A309444
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The successive approximations up to 5^n for 5-adic integer 4^(1/3).
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11
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0, 4, 9, 59, 559, 3059, 12434, 59309, 371809, 371809, 8184309, 27715559, 76543684, 320684309, 1541387434, 25955449934, 86990606184, 392166387434, 2680984746809, 14125076543684, 52272049199934, 338374344121809, 2245722976934309, 7014094558965559, 42776881424199934
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OFFSET
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0,2
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LINKS
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FORMULA
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a(0) = 0 and a(1) = 4, a(n) = a(n-1) + 3 * (a(n-1)^3 - 4) mod 5^n for n > 1.
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EXAMPLE
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a(1) = ( 4)_5 = 4,
a(2) = ( 14)_5 = 9,
a(3) = ( 214)_5 = 59,
a(4) = (4214)_5 = 559.
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PROG
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(PARI) {a(n) = truncate((4+O(5^n))^(1/3))}
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CROSSREFS
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Expansions of p-adic integers:
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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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