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 A341600 #15 Nov 27 2022 07:57:52
%S A341600 1,5,5,5,5,69,197,453,453,1477,3525,3525,3525,3525,3525,3525,134597,
%T A341600 396741,396741,1445317,1445317,1445317,9833925,26611141,60165573,
%U A341600 127274437,261492165,529927621,1066798533,2140540357,2140540357,2140540357,10730474949,27910344133
%N A341600 One of the two successive approximations up to 2^n for 2-adic integer sqrt(-3/5). This is the 1 (mod 4) case.
%C A341600 a(n) is the unique number k in [1, 2^n] and congruent to 1 mod 4 such that 5*k^2 + 3 is divisible by 2^(n+1).
%H A341600 Jianing Song, <a href="/A341600/b341600.txt">Table of n, a(n) for n = 2..1000</a>
%F A341600 a(2) = 1; for n >= 3, a(n) = a(n-1) if 5*a(n-1)^2 + 3 is divisible by 2^(n+1), otherwise a(n-1) + 2^(n-1).
%F A341600 a(n) = 2^n - A341601(n).
%F A341600 a(n) = Sum_{i=0..n-1} A341602(i)*2^i.
%F A341600 a(n) == Fibonacci(2^(2*n-1)) (mod 2^n). - _Peter Bala_, Nov 11 2022
%e A341600 The unique number k in [1, 4] and congruent to 1 modulo 4 such that 5*k^2 + 3 is divisible by 8 is 1, so a(2) = 1.
%e A341600 5*a(2)^2 + 3 = 8 which is not divisible by 16, so a(3) = a(2) + 2^2 = 5.
%e A341600 5*a(3)^2 + 3 = 128 which is divisible by 32, 64 and 128, so a(6) = a(5) = a(4) = a(3) = 5.
%e A341600 ...
%o A341600 (PARI) a(n) = truncate(-sqrt(-3/5+O(2^(n+1))))
%Y A341600 Cf. A341601 (the 3 (mod 4) case), A341602 (digits of the associated 2-adic square root of -3/5), A318960, A318961 (successive approximations of sqrt(-7)), A341538, A341539 (successive approximations of sqrt(17)).
%K A341600 nonn,easy
%O A341600 2,2
%A A341600 _Jianing Song_, Feb 16 2021