A130508 a(1)=2. a(2)=3. a(3)=1. a(n+3) = 3 + a(n), for all positive integers n.

2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 29, 30, 28, 32, 33, 31, 35, 36, 34, 38, 39, 37, 41, 42, 40, 44, 45, 43, 47, 48, 46, 50, 51, 49, 53, 54, 52, 56, 57, 55, 59, 60, 58, 62, 63, 61, 65, 66, 64, 68

Offset: 1

Author

Leroy Quet, Jun 01 2007

Keywords

• easy
• nonn

Comments

This sequence is a permutation of the positive integers, where each a(n) is the smallest positive integer not occurring earlier in the sequence such that the m-th term of the inverse permutation A130509 never equals a(m), for all positive integers m.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Crossrefs

Cf. A130509.

Programs

Mathematica

Transpose[NestList[{#[[2]],#[[3]],#[[1]]+3}&,{2,3,1},100]][[1]] (* Harvey P. Dale, Sep 08 2011 *)
LinearRecurrence[{1,0,1,-1},{2,3,1,5},100] (* Harvey P. Dale, Feb 02 2015 *)

Formula

a(1)=2, a(2)=3, a(3)=1, a(4)=5, a(n)=a(n-1)+a(n-3)-a(n-4). - Harvey P. Dale, Feb 02 2015

a(n) = n - 2*cos(2*n*Pi/3). - Wesley Ivan Hurt, Sep 27 2017

G.f.: x*(2+x-2*x^2+2*x^3) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 03 2021

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*Pi/(3*sqrt(3)) - log(2)/3. - Amiram Eldar, Jan 31 2023