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 A083523 #18 Jan 05 2025 19:51:37
%S A083523 1,2,8,8,144,46368,4807526976,51680708854858323072,
%T A083523 5972304273877744135569338397692020533504,
%U A083523 79757008057644623350300078764807923712509139103039448418553259155159833079730688
%N A083523 Smallest Fibonacci number divisible by 2^n.
%C A083523 The index of the Fibonacci numbers above begin: 1, 3, 6, 6 and then doubles thereafter.
%H A083523 Amiram Eldar, <a href="/A083523/b083523.txt">Table of n, a(n) for n = 0..12</a>
%H A083523 Ron Knott, <a href="https://r-knott.surrey.ac.uk/Fibonacci/fibtable.html#100">The first 300 Fibonacci numbers, completely factorised</a>.
%H A083523 Tamás Lengyel, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/33-3/lengyel.pdf">The order of the Fibonacci and Lucas numbers</a>, The Fibonacci Quarterly, Vol. 33, No. 3 (1995), pp. 234-239.
%F A083523 From _Amiram Eldar_, Jan 29 2022: (Start)
%F A083523 a(n) = Fibonacci(3*2^(n-2)) = A000045(A007283(n-2)) = A079613(n-2), for n > 2.
%F A083523 Sum_{n>=0} 1/a(n) = 19/8 - 1/phi, where phi is the golden ratio (A001622). (End)
%t A083523 Do[k = 1; While[ !IntegerQ[ Fibonacci[k]/2^n], k++ ]; Print[ Fibonacci[k]], {n, 0, 10}]
%t A083523 With[{fibs=Fibonacci[Range[1000]]},Table[SelectFirst[fibs, Divisible[#,2^n]&],{n,0,10}]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Feb 02 2021 *)
%t A083523 Join[{1, 2, 8}, Table[Fibonacci[3*2^(n - 2)], {n, 3, 9}]] (* _Amiram Eldar_, Jan 29 2022 *)
%Y A083523 Cf. A000045, A001622, A007283, A079613, A337923.
%K A083523 nonn
%O A083523 0,2
%A A083523 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 05 2003
%E A083523 Edited and extended by _Robert G. Wilson v_, May 06 2003