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 A191254 #19 May 31 2024 14:37:49
%S A191254 0,1,0,2,0,1,0,1,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,1,0,1,0,2,0,1,0,1,0,1,
%T A191254 0,2,0,1,0,1,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,1,0,1,0,2,0,1,0,2,0,1,0,2,
%U A191254 0,1,0,1,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,1,0,1,0,2,0,1,0,1,0,1,0,2,0,1,0,1,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,1,0,1,0,2,0,1,0,1,0,1,0,2
%N A191254 Fixed point of the morphism 0 -> 01, 1 -> 02, 2 -> 01.
%C A191254 For related sequences, see notes in the Mathematica program.
%C A191254 The asymptotic density of the occurrences of k = 0, 1 and 2 is 1/2, 1/3 and 1/6, respectively. The asymptotic mean of this sequence is 2/3. - _Amiram Eldar_, May 31 2024
%H A191254 Antti Karttunen, <a href="/A191254/b191254.txt">Table of n, a(n) for n = 1..65537</a>
%F A191254 From _Jianing Song_, May 30 2024: (Start)
%F A191254 Recurrence: a(2n-1) = 0, a(2n) = 1, 2, 1 for a(n) = 0, 1, 2 respectively.
%F A191254 a(n) = 0 for odd n; a(n) = 1 for even n such that v2(n) is odd; a(n) = 2 for even n such that v2(n) is even, where v2(n) = A007814(n) is the 2-adic valuation of n. (End)
%t A191254 t = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0, 2}, 2 -> {0, 1}}] &, {0}, 9] (* A191254 *)
%t A191254 Flatten[Position[t, 0]] (* A005408, the odds *)
%t A191254 a = Flatten[Position[t, 1]] (* A036554 *)
%t A191254 b = Flatten[Position[t, 2]] (* A108269 *)
%t A191254 a/2 (* A003159 *)
%t A191254 b/4 (* A003159 *)
%o A191254 (PARI) A191254(n) = if(n%2,0,if(valuation(n,2)%2,1,2)); \\ _Antti Karttunen_, Nov 06 2018
%Y A191254 Cf. A191250, A191255.
%Y A191254 Positions of 0 or 2: A003159; positions of 0: A005408; positions of 1: A036554; positions of 2: A108269.
%K A191254 nonn
%O A191254 1,4
%A A191254 _Clark Kimberling_, May 28 2011