A270641 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.

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, 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, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2

Offset

1,5

Comments

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

a(1) = 1, so the 2nd run has length 1, so a(5) must be 2 and a(6) = 1.
a(2) = 1, so the 3rd run has length 1, so a(7) = 2.
a(3) = 1, so the 4th run has length 1, so a(8) = 1.
a(4) = 1, so the 5th run has length 1, so a(9) = 2.
a(5) = 2, so the 6th run has length 2, so a(10) = 2 and a(11) = 1.
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.

Mathematica

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

Crossrefs

Cf. A000002, A006928, A022300,

Sequence in context: A080573 A186440 A006340 * A076371 A175044 A106149

Adjacent sequences: A270638 A270639 A270640 * A270642 A270643 A270644

Keyword

nonn,easy

Author

Clark Kimberling, Apr 05 2016

Status

approved