A270641 - OEIS

%I #10 Nov 22 2017 01:15:06

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

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

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

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

%C Guide to related sequences (with adjustments for initial terms):

%C 1, 1, 1, 1;    a(n) = length of (n + 1)st run of a; A270641

%C 1, 1, 1, 2;    a(n) = length of (n + 2)nd run of a; A270641

%C 1, 1, 2, 1;    a(n) = length of (n + 3)rd run of a; A270641

%C 1, 1, 2, 2;    a(n) = length of (n + 2)nd run of a; A270642

%C 1, 2, 1, 1;    a(n) = length of (n + 3)rd run of a; A022300

%C 1, 2, 1, 2;    a(n) = length of (n + 4)th run of a; A270641

%C 1, 2, 2, 1;    a(n) = length of (n + 3)rd run of a; A270643

%C 1, 2, 2, 2;    a(n) = length of (n + 2)nd run of a; A270644

%C 2, 1, 1, 1;    a(n) = length of (n + 2)nd run of a; A270645

%C 2, 1, 1, 2;    a(n) = length of (n + 3)rd run of a; A222300

%C 2, 1, 2, 1;    a(n) = length of (n + 4)th run of a; A270641

%C 2, 1, 2, 2;    a(n) = length of (n + 3)rd run of a; A000002 (Kolakoski)

%C 2, 2, 1, 1;    a(n) = length of (n + 2)nd run of a; A270646

%C 2, 2, 1, 2;    a(n) = length of (n + 3)rd run of a; A270647

%C 2, 2, 2, 1;    a(n) = length of (n + 2)nd run of a; A270644

%C 2, 2, 2, 2;    a(n) = length of (n + 1)st run of a; A270648

%H Clark Kimberling, <a href="/A270641/b270641.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 1, so the 2nd run has length 1, so a(5) must be 2 and a(6) = 1.

%e a(2) = 1, so the 3rd run has length 1, so a(7) = 2.

%e a(3) = 1, so the 4th run has length 1, so a(8) = 1.

%e a(4) = 1, so the 5th run has length 1, so a(9) = 2.

%e a(5) = 2, so the 6th run has length 2, so a(10) = 2 and a(11) = 1.

%e Globally, the runlength sequence of a is 4,1,1,1,1,2,1,2,1,2,2,1,...., and deleting the first term leaves a = A270641.

%t a = {1, 1, 1, 1};

%t Do[a = Join[a, ConstantArray[If[Last[a] == 1, 2, 1], {a[[n]]}]], {n,   200}]; a

%t (* _Peter J. C. Moses_, Apr 01 2016 *)

%Y Cf. A000002, A006928, A022300,

%K nonn,easy

%O 1,5

%A _Clark Kimberling_, Apr 05 2016