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 A322926 #23 Aug 30 2019 02:43:17 %S A322926 0,1,1,5,13,29,29,93,93,93,605,1629,3677,3677,3677,20061,20061,20061, %T A322926 151133,151133,151133,151133,151133,4345437,4345437,21122653,54677085, %U A322926 54677085,188894813,457330269,457330269,457330269,2604813917,6899781213,6899781213 %N A322926 The successive approximations up to 2^n for 2-adic integer 5^(1/3). %C A322926 a(n) is the unique solution to x^3 == 5 (mod 2^n) in the range [0, 2^n - 1]. %H A322926 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a> %F A322926 For n > 0, a(n) = a(n-1) if a(n-1)^3 - 5 is divisible by 2^n, otherwise a(n-1) + 2^(n-1). %e A322926 13^3 = 2197 = 137*2^4 + 5; %e A322926 29^3 = 24389 = 762*2^5 + 5 = 381*2^6 + 5; %e A322926 93^3 = 804357 = 6284*2^7 + 5 = 3142*2^8 + 5 = 1571*2^9 + 5. %o A322926 (PARI) a(n) = lift(sqrtn(5+O(2^n), 3)) %Y A322926 For the digits of 5^(1/3), see A323045. %Y A322926 Approximations of p-adic cubic roots: %Y A322926 A322701 (2-adic, 3^(1/3)); %Y A322926 this sequence (2-adic, 5^(1/3)); %Y A322926 A322934 (2-adic, 7^(1/3)); %Y A322926 A322999 (2-adic, 9^(1/3)); %Y A322926 A290567 (5-adic, 2^(1/3)); %Y A322926 A290568 (5-adic, 3^(1/3)); %Y A322926 A309444 (5-adic, 4^(1/3)); %Y A322926 A319097, A319098, A319199 (7-adic, 6^(1/3)); %Y A322926 A320914, A320915, A321105 (13-adic, 5^(1/3)). %K A322926 nonn %O A322926 0,4 %A A322926 _Jianing Song_, Aug 30 2019