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 A320914 #44 Aug 29 2019 10:23:37 %S A320914 0,7,7,1021,20794,77916,4533432,57628331,810610535,8967917745, %T A320914 40781415864,592215383260,22098140111704,208482821091552, %U A320914 3842984100198588,23529866028695033,586574689183693360,5244490953465952247,74447818308516655711,524269446116346228227,9295791188369022892289 %N A320914 One of the three successive approximations up to 13^n for 13-adic integer 5^(1/3). This is the 7 (mod 13) case (except for n = 0). %C A320914 For n > 0, a(n) is the unique number k in [1, 13^n] and congruent to 7 mod 13 such that k^3 - 5 is divisible by 13^n. %C A320914 For k not divisible by 13, k is a cube in 13-adic field if and only if k == 1, 5, 8, 12 (mod 13). If k is a cube in 13-adic field, then k has exactly three cubic roots. %H A320914 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a> %e A320914 The unique number k in [1, 13^2] and congruent to 7 modulo 13 such that k^3 - 5 is divisible by 13^2 is k = 7, so a(2) = 7. %e A320914 The unique number k in [1, 13^3] and congruent to 7 modulo 13 such that k^3 - 5 is divisible by 13^3 is k = 1021, so a(3) = 1021. %o A320914 (PARI) a(n) = lift(sqrtn(5+O(13^n), 3) * (-1+sqrt(-3+O(13^n)))/2) %Y A320914 Cf. A320915, A321105, A321106, A321107, A321108. %Y A320914 For 5-adic cubic roots, see A290567, A290568, A309444. %K A320914 nonn %O A320914 0,2 %A A320914 _Jianing Song_, Aug 27 2019