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A026185
If n even, then 2n. If n odd, then nearest integer to 2n/3.
5
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
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
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
CROSSREFS
Cf. A026184.
Bisections: A008586, A042968.
Sequence in context: A153016 A231549 A088610 * A026209 A198473 A133640
KEYWORD
nonn
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