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A270642 The sequence a of 1's and 2's starting with (1,1,2,2) such that a(n) is the length of the (n+2)nd run of a. 2

%I #6 Apr 07 2016 02:13:02

%S 1,1,2,2,1,2,1,1,2,2,1,2,2,1,2,1,1,2,2,1,2,2,1,1,2,1,1,2,1,2,2,1,1,2,

%T 1,1,2,2,1,2,1,1,2,1,2,2,1,2,2,1,1,2,1,2,2,1,2,1,1,2,2,1,2,2,1,2,1,1,

%U 2,1,1,2,2,1,2,2,1,1,2,1,2,2,1,2,2,1

%N The sequence a of 1's and 2's starting with (1,1,2,2) such that a(n) is the length of the (n+2)nd run of a.

%C See A270641 for a guide to related sequences.

%H Clark Kimberling, <a href="/A270642/b270642.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 1, so the 3rd run has length 1, so a(5) must be 1.

%e a(2) = 1, so the 4th run has length 1, so a(6) = 2 and a(7) = 1.

%e a(3) = 2, so the 5th run has length 2, so a(8) = 1 and a(9) = 2.

%e a(4) = 2, so the 6th run has length 2, so a(10) = 2 and a(11) = 1.

%e Globally, the runlength sequence is 2,2,1,1,2,2,1,2,1,1,2,2,1,2,..., and deleting the first 2 terms leaves the same sequence.

%t a = {1, 1, 2, 2}; Do[a = Join[a, ConstantArray[If[Last[a] == 1, 2, 1], {a[[n]]}]], {n, 200}]; a (* _Peter J. C. Moses_, Apr 01 2016 *)

%Y Cf. A000002, A006928, A022300, A270641.

%K nonn,easy

%O 1,3

%A _Clark Kimberling_, Apr 06 2016

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