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a(1)=2. a(2)=3. a(3)=1. a(n+3) = 3 + a(n), for all positive integers n.
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%I #22 Jan 31 2023 08:30:13

%S 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,

%T 25,29,30,28,32,33,31,35,36,34,38,39,37,41,42,40,44,45,43,47,48,46,50,

%U 51,49,53,54,52,56,57,55,59,60,58,62,63,61,65,66,64,68

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

%C 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.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).

%F 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

%F a(n) = n - 2*cos(2*n*Pi/3). - _Wesley Ivan Hurt_, Sep 27 2017

%F G.f.: x*(2+x-2*x^2+2*x^3) / ( (1+x+x^2)*(x-1)^2 ). - _R. J. Mathar_, Oct 03 2021

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

%t Transpose[NestList[{#[[2]],#[[3]],#[[1]]+3}&,{2,3,1},100]][[1]] (* _Harvey P. Dale_, Sep 08 2011 *)

%t LinearRecurrence[{1,0,1,-1},{2,3,1,5},100] (* _Harvey P. Dale_, Feb 02 2015 *)

%Y Cf. A130509.

%K easy,nonn

%O 1,1

%A _Leroy Quet_, Jun 01 2007