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 A341601 #18 Nov 27 2022 07:58:02
%S A341601 3,3,11,27,59,59,59,59,571,571,571,4667,12859,29243,62011,127547,
%T A341601 127547,127547,651835,651835,2748987,6943291,6943291,6943291,6943291,
%U A341601 6943291,6943291,6943291,6943291,6943291,2154426939,6449394235,6449394235,6449394235
%N A341601 One of the two successive approximations up to 2^n for 2-adic integer sqrt(-3/5). This is the 3 (mod 4) case.
%C A341601 a(n) is the unique number k in [1, 2^n] and congruent to 3 mod 4 such that 5*k^2 + 3 is divisible by 2^(n+1).
%H A341601 Jianing Song, <a href="/A341601/b341601.txt">Table of n, a(n) for n = 2..1000</a>
%F A341601 a(2) = 3; 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 A341601 a(n) = 2^n - A341600(n).
%F A341601 a(n) = Sum_{i = 0..n-1} A341603(i)*2^i.
%F A341601 a(n) == Fibonacci(4^n) (mod 2^n). - _Peter Bala_, Nov 11 2022
%e A341601 The unique number k in [1, 4] and congruent to 3 modulo 4 such that 5*k^2 + 3 is divisible by 8 is 3, so a(2) = 3.
%e A341601 5*a(2)^2 + 3 = 48 which is divisible by 16, so a(3) = a(2) = 3.
%e A341601 5*a(3)^2 + 3 = 48 which is not divisible by 32, so a(4) = a(3) + 2^3 = 11.
%e A341601 5*a(4)^2 + 3 = 608 which is not divisible by 64, so a(5) = a(4) + 2^4 = 27.
%e A341601 5*a(5)^2 + 3 = 3648 which is not divisible by 128, so a(6) = a(5) + 2^5 = 59.
%e A341601 ...
%o A341601 (PARI) a(n) = if(n==2, 3, truncate(sqrt(-3/5+O(2^(n+1)))))
%Y A341601 Cf. A145231, A341600 (the 1 (mod 4) case), A341603 (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 A341601 nonn,easy
%O A341601 2,1
%A A341601 _Jianing Song_, Feb 16 2021