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%I #10 Aug 03 2019 14:18:38
%S 0,4,9,59,559,3059,12434,59309,371809,371809,8184309,27715559,
%T 76543684,320684309,1541387434,25955449934,86990606184,392166387434,
%U 2680984746809,14125076543684,52272049199934,338374344121809,2245722976934309,7014094558965559,42776881424199934
%N The successive approximations up to 5^n for 5-adic integer 4^(1/3).
%F a(0) = 0 and a(1) = 4, a(n) = a(n-1) + 3 * (a(n-1)^3 - 4) mod 5^n for n > 1.
%e a(1) = ( 4)_5 = 4,
%e a(2) = ( 14)_5 = 9,
%e a(3) = ( 214)_5 = 59,
%e a(4) = (4214)_5 = 559.
%o (PARI) {a(n) = truncate((4+O(5^n))^(1/3))}
%Y Cf. A309443.
%Y Expansions of p-adic integers:
%Y A268922, A269590 (5-adic, sqrt(-4));
%Y A048898, A048899 (5-adic, sqrt(-1));
%Y A290567 (5-adic, 2^(1/3));
%Y A290568 (5-adic, 3^(1/3)).
%K nonn
%O 0,2
%A _Seiichi Manyama_, Aug 03 2019
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