A270647 The sequence a of 1's and 2's starting with (2,2,1,2) such that a(n) is the length of the (n+3)rd run of a.

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

Offset: 1

Author

Clark Kimberling, Apr 07 2016

Keywords

• nonn
• easy

Comments

See A270641 for a guide to related sequences.

Examples

			a(1) = 2, so the 4th run has length 2, so a(5) must be 1 and a(6) = 1.
a(2) = 2, so the 5th run has length 2, so a(7) = 2 and a(8) = 2.
a(3) = 1, so the 6th run has length 1, so a(9) = 1 and a(10) = 2.
Globally, the runlength sequence of a is 2,1,1,2,2,1,2,1,1,2,2,1,2,2,1,2,1,1,2,..., and deleting the first 3 terms leaves a = A270647.
		

Links

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

Crossrefs

Cf. A000002, A006928, A022300, A270641.

Programs

Mathematica

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

Formula

Conjecture: a(n) = A270643(n+1). - R. J. Mathar, Jun 21 2025