A191254 - OEIS

%I #19 May 31 2024 14:37:49

%S 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 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 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 Fixed point of the morphism 0 -> 01, 1 -> 02, 2 -> 01.

%C For related sequences, see notes in the Mathematica program.

%C 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 Antti Karttunen, <a href="/A191254/b191254.txt">Table of n, a(n) for n = 1..65537</a>

%F From _Jianing Song_, May 30 2024: (Start)

%F Recurrence: a(2n-1) = 0, a(2n) = 1, 2, 1 for a(n) = 0, 1, 2 respectively.

%F 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 t = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0, 2}, 2 -> {0, 1}}] &, {0}, 9]  (* A191254 *)

%t Flatten[Position[t, 0]]  (* A005408, the odds *)

%t a = Flatten[Position[t, 1]] (* A036554 *)

%t b = Flatten[Position[t, 2]] (* A108269 *)

%t a/2 (* A003159 *)

%t b/4 (* A003159 *)

%o (PARI) A191254(n) = if(n%2,0,if(valuation(n,2)%2,1,2)); \\ _Antti Karttunen_, Nov 06 2018

%Y Cf. A191250, A191255.

%Y Positions of 0 or 2: A003159; positions of 0: A005408; positions of 1: A036554; positions of 2: A108269.

%K nonn

%O 1,4

%A _Clark Kimberling_, May 28 2011