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

0,3

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

Table of n, a(n) for n=0..61.

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)

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

G.f.: x*(1 + 4*x + x^2 + 4*x^3 + x^4 + 4*x^5 + x^6)/(1 - x^2 - x^6 + x^8). - Charles R Greathouse IV, May 17 2026

Mathematica

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

Prog

(Magma) [IsEven(n) select 2*n else Round(2*n/3): n in [0..79] ]; // Vincenzo Librandi, Feb 03 2020
(PARI) a(n)=2*n\/if(n%2, 3, 1) \\ Charles R Greathouse IV, May 17 2026

Crossrefs

Cf. A026184.

Bisections: A008586, A042968.

Sequence in context: A153016 A231549 A088610 * A026209 A198473 A133640

Adjacent sequences: A026182 A026183 A026184 * A026186 A026187 A026188

Keyword

nonn,easy

Author

Clark Kimberling

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.

Status

approved