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 A325892 #8 Sep 11 2019 20:37:00 %S A325892 0,1,3,3,3,19,19,83,211,211,211,211,2259,6355,14547,30931,63699, %T A325892 129235,129235,129235,129235,129235,129235,4323539,4323539,4323539, %U A325892 4323539,4323539,4323539,4323539,4323539,4323539,2151807187,6446774483,6446774483,6446774483 %N A325892 The successive approximations up to 2^n for the 2-adic integer 3^(1/5). %C A325892 a(n) is the unique solution to x^5 == 3 (mod 2^n) in the range [0, 2^n - 1]. %H A325892 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a> %F A325892 For n > 0, a(n) = a(n-1) if a(n-1)^5 - 3 is divisible by 2^n, otherwise a(n-1) + 2^(n-1). %e A325892 For n = 2, the unique solution to x^5 == 3 (mod 4) in the range [0, 3] is x = 3, so a(2) = 3. %e A325892 a(2)^5 - 3 = 240 which is divisible by 8, so a(3) = a(2) = 3; %e A325892 a(3)^5 - 3 = 240 which is divisible by 16, so a(4) = a(3) = 3; %e A325892 a(4)^5 - 3 = 240 which is not divisible by 32, so a(5) = a(4) + 16 = 19; %e A325892 a(5)^5 - 3 = 2476096 which is divisible by 64, so a(6) = a(5) = 19. %o A325892 (PARI) a(n) = lift(sqrtn(3+O(2^n), 5)) %Y A325892 For the digits of 3^(1/5), see A325896. %Y A325892 Approximations of p-adic fifth-power roots: %Y A325892 this sequence (2-adic, 3^(1/5)); %Y A325892 A325893 (2-adic, 5^(1/5)); %Y A325892 A325894 (2-adic, 7^(1/5)); %Y A325892 A325895 (2-adic, 9^(1/5)); %Y A325892 A322157 (5-adic, 7^(1/5)); %Y A325892 A309450 (7-adic, 2^(1/5)); %Y A325892 A309451 (7-adic, 3^(1/5)); %Y A325892 A309452 (7-adic, 4^(1/5)); %Y A325892 A309453 (7-adic, 5^(1/5)); %Y A325892 A309454 (7-adic, 6^(1/5)). %K A325892 nonn %O A325892 0,3 %A A325892 _Jianing Song_, Sep 07 2019