A128173 Numbers in ternary reflected Gray code order.

0, 1, 2, 5, 4, 3, 6, 7, 8, 17, 16, 15, 12, 13, 14, 11, 10, 9, 18, 19, 20, 23, 22, 21, 24, 25, 26, 53, 52, 51, 48, 49, 50, 47, 46, 45, 36, 37, 38, 41, 40, 39, 42, 43, 44, 35, 34, 33, 30, 31, 32, 29, 28, 27, 54, 55, 56, 59, 58, 57, 60, 61, 62, 71, 70, 69, 66, 67, 68, 65, 64, 63, 72

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..19682

Donald E. Knuth, The Art of Computer Programming, Pre-Fascicle 2A, Draft of Section 7.2.1.1, subsection "Nonbinary Gray codes", page 18. At the bottom of page 19, ternary example g hat for all m_j=3 is the present sequence.

Z. Sunic, Tree morphisms, transducers and integer sequences, arXiv:math/0612080 [math.CO], 2006.

Index entries for sequences that are permutations of the natural numbers

Maple

A128173 := proc(nmax) local K, tmp, n3, n, r, c, t, a ; n3 := 3 ; n := 1 ; K := linalg[matrix](n3, 1, [[0], [1], [2]]) ; while n3 < nmax do n3 := n3*3 ; n := n+1 ; tmp := K ; K := linalg[extend](K, 2*n3/3, 1, 0) ; K := linalg[copyinto](tmp, K, 1+n3/3, 1) ; K := linalg[copyinto](tmp, K, 1+2*n3/3, 1) ; for r from 1 to n3 do K[r, n] := floor((r-1)/(n3/3)) ; od ; for r from n3/3+1 to n3/2 do for c from 1 to n do t := K[r, c] ; K[r, c] := K[n3+1-r, c] ; K[n3+1-r, c] := t ; od ; od ; od ; a := [] ; for r from 1 to n3 do a := [op(a), add( K[r, c]*3^(c-1), c=1..n) ] ; od ; a ; end: A128173(30) ; # R. J. Mathar, Jun 17 2007

Mathematica

a[n_] := Module[{v, r, i}, v = IntegerDigits[n, 3]; r = 0; For[i = 1, i <= Length[v], i++, If[r == 1, v[[i]] = 2 - v[[i]]]; r = Mod[r + v[[i]], 2]]; FromDigits[v, 3]];
a /@ Range[0, 100] (* Jean-François Alcover, Jul 18 2020, after Kevin Ryde *)

Prog

(PARI) a(n) = my(v=digits(n, 3), r=Mod(0, 2)); for(i=1, #v, if(r, v[i]=2-v[i]); r+=v[i]); fromdigits(v, 3); \\ Kevin Ryde, May 21 2020

Crossrefs

Cf. A003188, A105529, A105530.

Sequence in context: A222235 A163332 A275105 * A265362 A264989 A328625

Adjacent sequences: A128170 A128171 A128172 * A128174 A128175 A128176

Keyword

nonn

Author

Ralf Stephan, May 09 2007

Extensions

More terms from R. J. Mathar, Jun 17 2007

Offset changed to 0 by Alois P. Heinz, Feb 23 2018

Status

approved