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 A324082 #9 Sep 07 2019 19:08:54 %S A324082 0,3,68,575,13757,156562,4612078,52880168,178377202,9967145854, %T A324082 137221138330,1240089073122,22746013801566,279024950148857, %U A324082 2399150696294628,2399150696294628,104770936724476142,3431853982640375347,98586429095835092610,1335595905567366417029 %N A324082 One of the four successive approximations up to 13^n for 13-adic integer 3^(1/4).This is the 3 (mod 13) case (except for n = 0). %C A324082 For n > 0, a(n) is the unique number k in [1, 13^n] and congruent to 3 mod 13 such that k^4 - 3 is divisible by 13^n. %C A324082 For k not divisible by 13, k is a fourth power in 13-adic field if and only if k == 1, 3, 9 (mod 13). If k is a fourth power in 13-adic field, then k has exactly 4 fourth-power roots. %H A324082 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a> %F A324082 a(n) = A324077(n)*A286841(n) mod 13^n = A324084(n)*A286840(n) mod 13^n. %F A324082 For n > 0, a(n) = 13^n - A324083(n). %F A324082 a(n)^2 == A322086(n) (mod 13^n). %e A324082 The unique number k in [1, 13^2] and congruent to 3 modulo 13 such that k^4 - 3 is divisible by 13^2 is k = 68, so a(2) = 68. %e A324082 The unique number k in [1, 13^3] and congruent to 3 modulo 13 such that k^4 - 3 is divisible by 13^3 is k = 575, so a(3) = 575. %o A324082 (PARI) a(n) = lift(sqrtn(3+O(13^n), 4)) %Y A324082 Cf. A286840, A286841, A322085, A324077, A324083, A324084, A324085, A324086, A324087, A324153. %K A324082 nonn %O A324082 0,2 %A A324082 _Jianing Song_, Sep 01 2019