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

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, 52, 18, 56, 19, 60, 21, 64, 22, 68, 23, 72, 25, 76, 26, 80, 27, 84, 29, 88, 30, 92, 31, 96, 33, 100, 34, 104, 35, 108, 37, 112, 38, 116, 39, 120, 41

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Comments

For n > 0, position of n in A026184. In other words, this is the inverse permutation to A026184. For proof, see the Reble link.

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

Links

• F. M. Dekking, Permutations of N generated by left-right filling algorithms, arXiv:2001.08915 [math.CO], 2020.
• Don Reble, Proof that the two definitions are the same, Feb 01 2020
• Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,1,0,-1)

Crossrefs

Cf. A026184.

Bisections: A008586, A042968.

Programs

Magma

[IsEven(n) select 2*n else Round(2*n/3): n in [0..79] ]; // Vincenzo Librandi, Feb 03 2020

Mathematica

Table[If[EvenQ[n], 2 n, Round[2 n/3]], {n, 0, 50}] (* Vincenzo Librandi, Feb 03 2020 *)

Formula

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

Extensions

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.