A064579 Inverse permutation to A054082.

2, 1, 4, 3, 6, 8, 5, 10, 7, 12, 14, 9, 16, 18, 11, 20, 13, 22, 24, 15, 26, 17, 28, 30, 19, 32, 34, 21, 36, 23, 38, 40, 25, 42, 44, 27, 46, 29, 48, 50, 31, 52, 33, 54, 56, 35, 58, 60, 37, 62, 39, 64, 66, 41, 68, 43, 70, 72, 45, 74, 76, 47, 78, 49, 80, 82, 51, 84, 86, 53, 88, 55

Offset: 1

Author

N. J. A. Sloane, Oct 16 2001

Keywords

• nonn
• easy

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A054082.

Programs

Maple

A054082 := proc(nmax) local a,k,n,p ; a := [2,1] ; while nops(a) < nmax do n := nops(a)+1 : k := floor((n+1)/2) ; p := 1; while p in a do p := p+1 ; od ; if n mod 2 = 1 then a := [op(a), p+k-1] ; else a := [op(a), p] ; fi ; od ; RETURN(a) ; end: A064579 := proc(a054082) local a,n,ainv ; n := 1; a := [] ; while member(n,a054082,'ainv') do a := [op(a),ainv] ; n := n+1; od; RETURN(a) ; end: a054082 := A054082(200) : a064579 := A064579(a054082) : print(op(a064579)) ; # R. J. Mathar, Jun 27 2007

Mathematica

a[n_] := If[OddQ[n], Floor[((n+1)/2 - 1) GoldenRatio] + (n+1)/2 + 1, Floor[(n/2 - 1) GoldenRatio] + 2]; a[2] = 1;
Sort[Array[{a[#], #}&, 100]][[All, 2]] (* Jean-François Alcover, Apr 01 2020 *)

Extensions

Corrected and extended by R. J. Mathar, Jun 27 2007