cp's OEIS Frontend

A269594 a(n) = (A269590(n)^2 + 4)/5^n, n >= 0.

%I A269594 #14 Jan 12 2025 04:56:23
%S A269594 4,4,8,104,212,313,11645,2329,73757,160772,646925,129385,25877,
%T A269594 49838696,2503218301,16177487972,18226737365,3645347473,2526514341077,
%U A269594 2510040201736,43137313790909,136233128831473,1960924754787877,1733911367978596,27260145118408781
%N A269594 a(n) = (A269590(n)^2 + 4)/5^n, n >= 0.
%C A269594 a(n) is an integer because b(n) = A269590(n) satisfies b(n)^2 + 4 == 0 (mod 5^n), n>=0.
%C A269594 See A268922 for details and references.
%H A269594 Andrew Howroyd, <a href="/A269594/b269594.txt">Table of n, a(n) for n = 0..500</a>
%F A269594 a(n) = (b(n)^2 + 4)/5^n, n>=0, with b(n) = A269590(n).
%e A269594 a(0) = (0 + 4)/1 = 4.
%e A269594 a(4)= (364^2 + 4)/5^4 = 212.
%o A269594 (PARI) b(n) = if (n==0, 0, 5^n - truncate(sqrt(-4+O(5^(n)))));
%o A269594 a(n) = (b(n)^2 + 4)/5^n; \\ _Michel Marcus_, Mar 24 2016
%Y A269594 Cf. A268922, A269590, A269593 (companion).
%K A269594 nonn,easy
%O A269594 0,1
%A A269594 _Wolfdieter Lang_, Mar 02 2016
%E A269594 Terms a(21) and beyond from _Andrew Howroyd_, Mar 02 2020