This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A322701 #13 Aug 30 2019 02:44:33 %S A322701 0,1,3,3,11,27,59,123,123,379,379,379,379,4475,12667,29051,61819, %T A322701 127355,127355,127355,127355,127355,2224507,2224507,2224507,19001723, %U A322701 52556155,119665019,253882747,253882747,253882747,1327624571,3475108219,7770075515 %N A322701 The successive approximations up to 2^n for 2-adic integer 3^(1/3). %C A322701 a(n) is the unique solution to x^3 == 3 (mod 2^n) in the range [0, 2^n - 1]. %H A322701 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a> %F A322701 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 A322701 11^3 = 1331 = 83*2^4 + 3; %e A322701 27^3 = 19683 = 615*2^5 + 3; %e A322701 59^3 = 205379 = 3209*2^6 + 3. %o A322701 (PARI) a(n) = lift(sqrtn(3+O(2^n), 3)) %Y A322701 For the digits of 3^(1/3), see A323000. %Y A322701 Approximations of p-adic cubic roots: %Y A322701 this sequence (2-adic, 3^(1/3)); %Y A322701 A322926 (2-adic, 5^(1/3)); %Y A322701 A322934 (2-adic, 7^(1/3)); %Y A322701 A322999 (2-adic, 9^(1/3)); %Y A322701 A290567 (5-adic, 2^(1/3)); %Y A322701 A290568 (5-adic, 3^(1/3)); %Y A322701 A309444 (5-adic, 4^(1/3)); %Y A322701 A319097, A319098, A319199 (7-adic, 6^(1/3)); %Y A322701 A320914, A320915, A321105 (13-adic, 5^(1/3)). %K A322701 nonn %O A322701 0,3 %A A322701 _Jianing Song_, Aug 30 2019