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

1,1

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

Table of n, a(n) for n=1..67.

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

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

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 *)

Crossrefs

Cf. A130509.

Sequence in context: A195508 A049274 A339470 * A341635 A182938 A329445

Adjacent sequences: A130505 A130506 A130507 * A130509 A130510 A130511

Keyword

easy,nonn

Author

Leroy Quet, Jun 01 2007

Status

approved