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 A269593 #18 Jan 12 2025 04:56:44 %S A269593 4,1,5,1,109,1460,292,53476,124904,993169,5385572,43930532,239139524, %T A269593 777233593,789206948,2256445369,65340851012,661111023620,132222204724, %U A269593 7745142596633,10225443529556,103321258570120,20664251714024,4562022446935993,6246398287209928,20888388201358465 %N A269593 a(n) = (A268922(n)^2 + 4)/5^n, n >= 0. %C A269593 a(n) is an integer because b(n) = A268922(n) satisfies b(n)^2 + 4 == 0 (mod 5^n), n>=0. %C A269593 See A268922 for details and references. %H A269593 Andrew Howroyd, <a href="/A269593/b269593.txt">Table of n, a(n) for n = 0..500</a> %F A269593 a(n) = (b(n)^2 + 1)/5^n, n>=0, with b(n) = A268922(n). %e A269593 a(0) = (0 + 4)/1 = 4. %e A269593 a(4) = (261^2 + 4)/5^4 = 109. %o A269593 (PARI) a(n) = ((truncate(sqrt(-4+O(5^(n)))))^2 + 4)/5^n; \\ _Michel Marcus_, Mar 07 2016 %Y A269593 Cf. A268922, A269590, A269594 (companion sequence). %K A269593 nonn,easy %O A269593 0,1 %A A269593 _Wolfdieter Lang_, Mar 02 2016 %E A269593 Terms a(21) and beyond from _Andrew Howroyd_, Mar 02 2020