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 A322999 #44 Aug 30 2019 02:43:43 %S A322999 0,1,1,1,9,25,25,25,25,281,281,281,281,4377,4377,20761,53529,53529, %T A322999 184601,446745,971033,2019609,4116761,8311065,8311065,25088281, %U A322999 58642713,125751577,259969305,259969305,259969305,259969305,259969305,4554936601,13144871193 %N A322999 The successive approximations up to 2^n for 2-adic integer 9^(1/3). %C A322999 a(n) is the unique solution to x^3 == 9 (mod 2^n) in the range [0, 2^n - 1]. %H A322999 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a> %F A322999 For n > 0, a(n) = a(n-1) if a(n-1)^3 - 9 is divisible by 2^n, otherwise a(n-1) + 2^(n-1). %e A322999 9^3 = 729 = 45*2^4 + 9; %e A322999 25^3 = 15625 = 488*2^5 + 9 = 244*2^6 + 9 = 122*2^7 + 9 = 61*2^8 + 9; %e A322999 281^3 = 22188041 = 43336*2^9 + 9 = 21668*2^10 + 9 = 10834*2^11 + 9 = 5417*2^12 + 9. %o A322999 (PARI) a(n) = lift(sqrtn(9+O(2^n), 3)) %Y A322999 For the digits of 9^(1/3), see A323096. %Y A322999 Approximations of p-adic cubic roots: %Y A322999 A322701 (2-adic, 3^(1/3)); %Y A322999 A322926 (2-adic, 5^(1/3)); %Y A322999 A322934 (2-adic, 7^(1/3)); %Y A322999 this sequence (2-adic, 9^(1/3)); %Y A322999 A290567 (5-adic, 2^(1/3)); %Y A322999 A290568 (5-adic, 3^(1/3)); %Y A322999 A309444 (5-adic, 4^(1/3)); %Y A322999 A319097, A319098, A319199 (7-adic, 6^(1/3)); %Y A322999 A320914, A320915, A321105 (13-adic, 5^(1/3)). %K A322999 nonn %O A322999 0,5 %A A322999 _Jianing Song_, Aug 30 2019