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 A325894 #10 Sep 11 2019 20:37:25 %S A325894 0,1,3,7,7,7,39,103,231,231,743,1767,1767,1767,1767,18151,18151,18151, %T A325894 18151,18151,542439,1591015,3688167,7882471,16271079,33048295, %U A325894 66602727,133711591,267929319,267929319,804800231,804800231,804800231,804800231,9394734823,26574604007 %N A325894 The successive approximations up to 2^n for the 2-adic integer 7^(1/5). %C A325894 a(n) is the unique solution to x^5 == 7 (mod 2^n) in the range [0, 2^n - 1]. %H A325894 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a> %F A325894 For n > 0, a(n) = a(n-1) if a(n-1)^5 - 7 is divisible by 2^n, otherwise a(n-1) + 2^(n-1). %e A325894 For n = 2, the unique solution to x^5 == 7 (mod 4) in the range [0, 3] is x = 3, so a(2) = 3. %e A325894 a(2)^5 - 7 = 236 which is not divisible by 8, so a(3) = a(2) + 4 = 7; %e A325894 a(3)^5 - 7 = 16800 which is divisible by 16, so a(4) = a(3) = 7; %e A325894 a(4)^5 - 7 = 16800 which is divisible by 32, so a(5) = a(4) = 7; %e A325894 a(5)^5 - 7 = 16800 which is not divisible by 64, so a(6) = a(5) + 32 = 39. %o A325894 (PARI) a(n) = lift(sqrtn(7+O(2^n), 5)) %Y A325894 For the digits of 7^(1/5), see A325898. %Y A325894 Approximations of p-adic fifth-power roots: %Y A325894 A325892 (2-adic, 3^(1/5)); %Y A325894 A325893 (2-adic, 5^(1/5)); %Y A325894 this sequence (2-adic, 7^(1/5)); %Y A325894 A325895 (2-adic, 9^(1/5)); %Y A325894 A322157 (5-adic, 7^(1/5)); %Y A325894 A309450 (7-adic, 2^(1/5)); %Y A325894 A309451 (7-adic, 3^(1/5)); %Y A325894 A309452 (7-adic, 4^(1/5)); %Y A325894 A309453 (7-adic, 5^(1/5)); %Y A325894 A309454 (7-adic, 6^(1/5)). %K A325894 nonn %O A325894 0,3 %A A325894 _Jianing Song_, Sep 07 2019