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 A210853 #18 Jan 15 2025 01:44:33
%S A210853 1,4,608,100082,1033865,147695,363432817,493771113103,2362056468993,
%T A210853 408352474516087,11132773648769182,1051698129414636470,
%U A210853 55996715400581424222,4972138747809482684591,29726859239716779753649,180817068189496094994710,34294232575354274959952776,358207669631705219617812791
%N A210853 a(n) = (A210852(n)^3 + 1)/7^n, n >= 0.
%C A210853 a(n) is an integer because A210852(n) is one of the three solutions of X(n)^3 + 1 == 0 (mod 7^n), namely the one satisfying also X(n) == 3 (mod 7).
%C A210853 See the comments on A210852, and the Nagell reference given in A210848.
%H A210853 Paolo Xausa, <a href="/A210853/b210853.txt">Table of n, a(n) for n = 0..500</a>
%F A210853 a(n) = (b(n)^3 + 1)/7^n, n>=0, with b(n):=A210852(n) given by a recurrence. See also a Maple program for b(n) there.
%e A210853 a(0) = 1/1 = 1.
%e A210853 a(3) = (325^3 + 1)/7^3 = 34328126/343 = 100082, (b(3) = 31^7 (mod 7^3) = 325).
%t A210853 Join[{1}, MapIndexed[(#^3 + 1)/7^#2[[1]] &, FoldList[PowerMod[#, 7, 7^#2] &, 3, Range[2, 20]]]] (* _Paolo Xausa_, Jan 14 2025 *)
%Y A210853 Cf. A210848, A210849 (the p=5 case).
%K A210853 nonn,easy
%O A210853 0,2
%A A210853 _Wolfdieter Lang_, May 02 2012