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%I #13 Aug 30 2019 02:44:33
%S 0,1,3,3,11,27,59,123,123,379,379,379,379,4475,12667,29051,61819,
%T 127355,127355,127355,127355,127355,2224507,2224507,2224507,19001723,
%U 52556155,119665019,253882747,253882747,253882747,1327624571,3475108219,7770075515
%N The successive approximations up to 2^n for 2-adic integer 3^(1/3).
%C a(n) is the unique solution to x^3 == 3 (mod 2^n) in the range [0, 2^n - 1].
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F For n > 0, a(n) = a(n-1) if a(n-1)^3 - 3 is divisible by 2^n, otherwise a(n-1) + 2^(n-1).
%e 11^3 = 1331 = 83*2^4 + 3;
%e 27^3 = 19683 = 615*2^5 + 3;
%e 59^3 = 205379 = 3209*2^6 + 3.
%o (PARI) a(n) = lift(sqrtn(3+O(2^n), 3))
%Y For the digits of 3^(1/3), see A323000.
%Y Approximations of p-adic cubic roots:
%Y this sequence (2-adic, 3^(1/3));
%Y A322926 (2-adic, 5^(1/3));
%Y A322934 (2-adic, 7^(1/3));
%Y A322999 (2-adic, 9^(1/3));
%Y A290567 (5-adic, 2^(1/3));
%Y A290568 (5-adic, 3^(1/3));
%Y A309444 (5-adic, 4^(1/3));
%Y A319097, A319098, A319199 (7-adic, 6^(1/3));
%Y A320914, A320915, A321105 (13-adic, 5^(1/3)).
%K nonn
%O 0,3
%A _Jianing Song_, Aug 30 2019
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