cp's OEIS Frontend

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.

A321106 Digits of one of the three 13-adic integers 5^(1/3) that is related to A320914.

This page as a plain text file.
%I A321106 #13 Aug 28 2019 12:13:25
%S A321106 7,0,6,9,2,12,11,12,10,3,4,12,8,12,5,11,7,8,4,6,4,3,4,12,11,9,12,1,11,
%T A321106 5,7,10,9,5,10,2,6,11,12,6,11,6,12,8,6,11,12,7,3,2,9,5,1,12,0,5,10,3,
%U A321106 0,2,8,3,11,10,10,2,3,11,7,1,5,4,11,10,9,9,6,3,6,0,7
%N A321106 Digits of one of the three 13-adic integers 5^(1/3) that is related to A320914.
%C A321106 For k not divisible by 5, 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 A321106 Seiichi Manyama, <a href="/A321106/b321106.txt">Table of n, a(n) for n = 0..10000</a>
%H A321106 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>
%F A321106 a(n) = (A320914(n+1) - A320914(n))/13^n.
%e A321106 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 = (607)_13, so the first three terms are 7, 0 and 6.
%o A321106 (PARI) a(n) = lift(sqrtn(5+O(13^(n+1)), 3) * (-1+sqrt(-3+O(13^(n+1))))/2)\13^n
%Y A321106 Cf. A320914, A320915, A321105, A321107, A321108.
%Y A321106 For 5-adic cubic roots, see A290566, A290563, A309443.
%K A321106 nonn,base
%O A321106 0,1
%A A321106 _Jianing Song_, Aug 27 2019