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 A212155 #23 Jan 14 2025 16:27:50
%S A212155 5,2,0,3,6,4,0,4,2,3,2,2,1,4,5,4,5,2,0,5,5,3,1,6,4,3,2,5,3,2,3,1,0,0,
%T A212155 4,4,4,6,4,2,6,0,0,5,1,2,5,4,3,2,5,3,2,6,3,3,4,2,2,2,1,5,6,2,6,4,6,3,
%U A212155 5,6,4,0,5,1,4,1,1,0,6,0,4,2,2,4,5,0,3,2,1,1,5,6,2,4,2,2,1,1,5,3
%N A212155 Digits of one of the three 7-adic integers (-1)^(1/3).
%C A212155 See A210853 for comments and an approximation to this 7-adic number, called there v. See also A048898 for references on p-adic numbers.
%C A212155 a(n), n>=1, is the (unique) solution of the linear congruence 3 * b(n)^2 * a(n) + c(n) == 0 (mod 7), with b(n):=A212153(n) and c(n):=A212154(n). a(0) = 5, one of the three solutions of X^3+1 == 0 (mod 7).
%C A212155 Since b(n) == 5 (mod 7), a(n) == 4 * c(n) (mod 7) for n>0. - _Álvar Ibeas_, Feb 20 2017
%C A212155 With a(0) = 4, this is the digits of one of the three cube root of 1, the one that is congruent to 4 modulo 7. - _Jianing Song_, Aug 26 2022
%H A212155 Paolo Xausa, <a href="/A212155/b212155.txt">Table of n, a(n) for n = 0..10000</a>
%F A212155 a(n) = (b(n+1) - b(n))/7^n, n>=1, with b(n):=A212153(n), defined by a recurrence given there. One also finds there a Maple program for b(n). a(0)=5.
%F A212155 a(n) = 6 - A212152(n), for n>0. - _Álvar Ibeas_, Feb 21 2017
%t A212155 Join[{5}, MapIndexed[#/7^#2[[1]] &, Differences[FoldList[PowerMod[#, 7, 7^#2] &, 5, Range[2, 100]]]]] (* _Paolo Xausa_, Jan 14 2025 *)
%Y A212155 Cf. A212153 (approximations of (-1)^(1/3)), A212152 (digits of another cube root of -1), 6*A000012 (digits of -1).
%Y A212155 Cf. A210850, A210851 (digits of the 5-adic integers sqrt(-1)); A319297, A319305, A319555 (digits of the 7-adic integers 6^(1/3)).
%K A212155 nonn,easy
%O A212155 0,1
%A A212155 _Wolfdieter Lang_, May 02 2012