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 A332937 #14 Jan 15 2025 16:43:10
%S A332937 1,1,2,3,4,1,1,1,2,1,1,1,3,1,2,5,1,1,6,1,1,7,1,1,8,1,1,9,2,1,10,1,1,
%T A332937 11,2,1,1,1,1,1,2,1,3,1,4,1,2,1,1,1,2,3,1,1,2,5,4,3,1,1,2,1,1,1,1,1,6,
%U A332937 1,1,1,2,1,2,1,1,1,4,7,1,1,1,3,2,1,1,1,2,1,8,1,3,1,2,1,1,5,12,1,2,1,1,1,2,1,13,3,1,1
%N A332937 a(n) is the greatest common divisor of the first two terms of row n of the Wythoff array (A035513).
%C A332937 a(n) is also the gcd of every pair of consecutive terms of row n of the Wythoff array. Conjectures: the maximal number of consecutive 1's is 5, and the limiting proportion of 1's exists. See A332938.
%C A332937 If seems that for all primes p > 3, a(1+p) = 1. - _Antti Karttunen_, Jan 15 2025
%H A332937 Antti Karttunen, <a href="/A332937/b332937.txt">Table of n, a(n) for n = 1..20000</a>
%e A332937 See A332938.
%t A332937 W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k]; (* A035513 *)
%t A332937 t = Table[GCD[W[n, 1], W[n, 2]], {n, 1, 160}] (* A332937 *)
%t A332937 Flatten[Position[t, 1]] (* A332938 *)
%o A332937 (PARI) T(n, k) = (n+sqrtint(5*n^2))\2*fibonacci(k+1) + (n-1)*fibonacci(k); \\ A035513
%o A332937 a(n) = gcd(T(n, 0), T(n, 1)); \\ _Michel Marcus_, Mar 03 2020
%Y A332937 Cf. A000045, A173027, A173028, A035513, A332938 (positions of 1's).
%K A332937 nonn,easy
%O A332937 1,3
%A A332937 _Clark Kimberling_, Mar 03 2020
%E A332937 More terms from _Antti Karttunen_, Jan 15 2025