cp's OEIS Frontend

A026185 If n even, then 2n. If n odd, then nearest integer to 2n/3.

%I A026185 #24 Sep 08 2022 08:44:49
%S A026185 0,1,4,2,8,3,12,5,16,6,20,7,24,9,28,10,32,11,36,13,40,14,44,15,48,17,
%T A026185 52,18,56,19,60,21,64,22,68,23,72,25,76,26,80,27,84,29,88,30,92,31,96,
%U A026185 33,100,34,104,35,108,37,112,38,116,39,120,41
%N A026185 If n even, then 2n. If n odd, then nearest integer to 2n/3.
%C A026185 For n > 0, position of n in A026184. In other words, this is the inverse permutation to A026184. For proof, see the Reble link.
%C A026185 Permutation of nonnegative integers: lodumo_4 of (0,1,0,2,0,3,0,1,0,2,0,3,0,1,0,2,0,3,0,1,0,2,0,3,0,1,0,2,0,3,...). - _Philippe Deléham_, Oct 25 2011
%H A026185 F. M. Dekking, <a href="https://arxiv.org/abs/2001.08915">Permutations of N generated by left-right filling algorithms</a>, arXiv:2001.08915 [math.CO], 2020.
%H A026185 Don Reble, <a href="/A026185/a026185.txt">Proof that the two definitions are the same</a>, Feb 01 2020
%H A026185 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,1,0,-1)
%F A026185 a(2n)=4n; a(6n+1)=4n+1; a(6n+3)=4n+2; a(6n+5)=4n+3. G.f.: x(1+4*x+x^2+4*x^3+x^4+4*x^5+x^6)/((1+x^2+x^4)*(1-x^2)^2). - _Philippe Deléham_, Oct 25 2011
%t A026185 Table[If[EvenQ[n], 2 n, Round[2 n/3]], {n, 0, 50}] (* _Vincenzo Librandi_, Feb 03 2020 *)
%o A026185 (Magma) [IsEven(n) select 2*n else Round(2*n/3): n in [0..79] ]; // _Vincenzo Librandi_, Feb 03 2020
%Y A026185 Cf. A026184.
%Y A026185 Bisections: A008586, A042968.
%K A026185 nonn
%O A026185 0,3
%A A026185 _Clark Kimberling_
%E A026185 Edited by _N. J. A. Sloane_, Feb 02 2020, changing the definition to one given by _Philippe Deléham_, Oct 25 2011, and making the old definition a comment. Thanks to _Don Reble_ for proving that the two definitions produce the same sequence.