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 A322934 #19 Aug 30 2019 02:43:30 %S A322934 0,1,3,7,7,23,23,23,151,407,407,1431,3479,3479,11671,11671,44439, %T A322934 109975,241047,503191,1027479,2076055,2076055,6270359,6270359,6270359, %U A322934 6270359,6270359,6270359,274705815,811576727,1885318551,1885318551,6180285847 %N A322934 The successive approximations up to 2^n for 2-adic integer 7^(1/3). %C A322934 a(n) is the unique solution to x^3 == 7 (mod 2^n) in the range [0, 2^n - 1]. %H A322934 Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a> %F A322934 For n > 0, a(n) = a(n-1) if a(n-1)^3 - 7 is divisible by 2^n, otherwise a(n-1) + 2^(n-1). %e A322934 7^3 = 343 = 21*2^4 + 7; %e A322934 23^3 = 12167 = 380*2^5 + 7 = 190*2^6 + 7 = 95*2^7 + 7; %e A322934 151^3 = 3442951 = 13449*2^8 + 7. %o A322934 (PARI) a(n) = lift(sqrtn(7+O(2^n), 3)) %Y A322934 For the digits of 7^(1/3), see A323095. %Y A322934 Approximations of p-adic cubic roots: %Y A322934 A322701 (2-adic, 3^(1/3)); %Y A322934 A322926 (2-adic, 5^(1/3)); %Y A322934 this sequence (2-adic, 7^(1/3)); %Y A322934 A322999 (2-adic, 9^(1/3)); %Y A322934 A290567 (5-adic, 2^(1/3)); %Y A322934 A290568 (5-adic, 3^(1/3)); %Y A322934 A309444 (5-adic, 4^(1/3)); %Y A322934 A319097, A319098, A319199 (7-adic, 6^(1/3)); %Y A322934 A320914, A320915, A321105 (13-adic, 5^(1/3)). %K A322934 nonn %O A322934 0,3 %A A322934 _Jianing Song_, Aug 30 2019