A143097 3*k - 2 interleaved with 3*k - 1 and 3*k.

1, 2, 4, 3, 5, 7, 6, 8, 10, 9, 11, 13, 12, 14, 16, 15, 17, 19, 18, 20, 22, 21, 23, 25, 24, 26, 28, 27, 29, 31, 30, 32, 34, 33, 35, 37, 36, 38, 40, 39, 41, 43, 42, 44, 46, 45, 47, 49, 48, 50, 52, 51, 53, 55, 54, 56, 58, 57, 59, 61, 60, 62, 64, 63, 65, 67, 66

Offset

1,2

Comments

First differences give A143098.

Binomial transform = A143099: (1, 3, 9, 22, 50, 113, 256, ...).

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Formula

A permutation of the natural numbers: 3*k - 2 interleaved with 3*k - 1 and 3*k; k=1,2,3,...; given a(1) = 1. a(n) = n if the subset = 3*k - 1: (2, 5, 8, ...); a(n) = n+1 in 3*k - 2, k>1: (4, 7, 10, ...); and a(n) = (n-1) in 3*k: (3, 6, 9, ...).

G.f.: x(1+x+2x^2-2x^3+x^4)/((1-x)^2(1+x+x^2)). - R. J. Mathar, Sep 06 2008

a(n) = if(n==1, 1, (n-1) + (n-1) mod 3). - Zak Seidov, Feb 23 2017

For n>1, a(n) = n+2*sin(2*(n+1)*Pi/3)/sqrt(3). - Wesley Ivan Hurt, Sep 27 2017

Sum_{n>=1} (-1)^(n+1)/a(n) = 2 - 2*Pi/(3*sqrt(3)) - log(2)/3. - Amiram Eldar, Aug 21 2023

Example

Interleave 3 subsets:
  1,....4,.......7,......10,......13,......16,...
  ...2,.......5,.......8,......11,......14,...
  .........3,.......6,.......9,......12,...
  ...

Maple

A143097 := proc(n) if(n<=1)then return n: elif(n mod 3 <= 1)then return n+1-2*(n mod 3): else return n: fi: end: seq(A143097(n), n=1..70); # Nathaniel Johnston, Apr 30 2011

Mathematica

With[{nn=70}, Join[{1}, Riffle[Rest[Select[Range[nn], !Divisible[#, 3]&]], Range[ 3, nn, 3], 3]]] (* Harvey P. Dale, May 06 2012 *)
Table[If[k == 1, 1, k - 1 + Mod[k - 1, 3]], {k, 100}] (* Zak Seidov, Feb 23 2017 *)

Crossrefs

Cf. A115302, A143098, A143099.

Cf. A083220 (n + (n mod 4)). - Zak Seidov, Feb 23 2017

Sequence in context: A074146 A262478 A236348 * A074147 A138607 A372341

Adjacent sequences: A143094 A143095 A143096 * A143098 A143099 A143100

Keyword

easy,nonn

Author

Gary W. Adamson, Jul 24 2008

Status

approved