A105530 -id:A105530 - cp's OEIS frontend

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

Ralf Stephan, May 09 2007

nonn

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

Cf. A003188, A105529, A105530.

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

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 *)

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

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

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

A105529 Given a list of ternary numbers, interpret each as a ternary modular Gray code number, then convert to decimal.

Original entry on oeis.org

0, 1, 2, 4, 5, 3, 8, 6, 7, 13, 14, 12, 17, 15, 16, 9, 10, 11, 26, 24, 25, 18, 19, 20, 22, 23, 21, 40, 41, 39, 44, 42, 43, 36, 37, 38, 53, 51, 52, 45, 46, 47, 49, 50, 48, 27, 28, 29, 31, 32, 30, 35, 33, 34, 80, 78, 79, 72, 73, 74, 76, 77, 75

Offset: 0

Gary W. Adamson, Apr 11 2005

			a(9) = 13 since Ternary 100 (9 decimal) interpreted as Ternary Gray code = 13.

Index entries for sequences that are permutations of the natural numbers

Cf. A105530 (inverse), A128173 (ternary reflected), A006068 (binary), A226134 (decimal modular), A007089.

a[n_] := Module[{v = IntegerDigits[n, 3]}, Do[v[[i]] = Mod[v[[i]]+v[[i-1]], 3], {i, 2, Length[v]}]; FromDigits[v, 3]];
Table[a[n], {n, 0, 62}] (* Jean-François Alcover, Jun 26 2023, after Kevin Ryde *)

a(n) = my(v=digits(n,3)); for(i=2,#v, v[i]=(v[i]+v[i-1])%3); fromdigits(v,3); \\ Kevin Ryde, May 23 2020

More terms from Sean A. Irvine, Feb 09 2012

Comments by Gary W. Adamson moved to A105530 where they better apply. - Kevin Ryde, May 30 2020

A098488 Decimal modular Gray code for n.

Original entry on oeis.org

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

Offset: 0

Jaume Simon Gispert (jaume(AT)nuem.com), Sep 10 2004

This is another decimal Gray code that considers that the distance between 9 and 0 is 1. Cyclic for (left-zero-padded) groups of n digits.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Martin Cohn, Affine m-ary Gray Codes, Information and Control, volume 6, 1963, pages 70-78. Example 4 column "Gray" is the present sequence.
Donald E. Knuth, The Art of Computer Programming, Pre-Fascicle 2A, Draft of Section 7.2.1.1. See subsection "Nonbinary Gray codes" page 18, and exercise 78 page 35 and answer page 54 (modular Gray g overline (k) for the case all m_j=10).
Index entries for sequences that are permutations of the natural numbers

Cf. A003100.

Cf. A226134 (inverse).

import Data.List (elemIndex); import Data.Maybe (fromJust)
a098488 = fromJust . (`elemIndex` a226134_list)
-- Reinhard Zumkeller, Jun 03 2013

# insert 10 into the second argument of the gray(.,.) function in A105530. - R. J. Mathar, Mar 10 2015

AltGray[In_] := { tIn = IntegerDigits[In]; Ac = 0; Do[tIn[[z]] = Mod[tIn[[z]] - Ac, 10]; Ac += tIn[[z]], {z, 1, Length[tIn]}]; FromDigits[tIn, 10] }

a(n) = my(v=digits(n)); forstep(i=#v,2,-1, v[i]=(v[i]-v[i-1])%10); fromdigits(v); \\ Kevin Ryde, May 15 2020

A381668 Ternary modular Gray code for n written in base 3.

Original entry on oeis.org

0, 1, 2, 12, 10, 11, 21, 22, 20, 120, 121, 122, 102, 100, 101, 111, 112, 110, 210, 211, 212, 222, 220, 221, 201, 202, 200, 1200, 1201, 1202, 1212, 1210, 1211, 1221, 1222, 1220, 1020, 1021, 1022, 1002, 1000, 1001, 1011, 1012, 1010, 1110, 1111, 1112, 1122, 1120, 1121

Offset: 0

Joshua Chester, Mar 03 2025

Similar to binary Gray code in that a(n) differs from a(n+1) by one digit, including the last number with a given number of digits compared to a(0).

Cf. A007089, A105530.

a(n) = my(v=digits(n, 3)); forstep(i=#v, 2, -1, v[i]=(v[i]-v[i-1])%3); fromdigits(v, 10); \\ (after A105530) - Andrew Howroyd, Mar 03 2025

a(n) = A007089(A105530(n)).

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A128173 Numbers in ternary reflected Gray code order.

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A105529 Given a list of ternary numbers, interpret each as a ternary modular Gray code number, then convert to decimal.

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A098488 Decimal modular Gray code for n.

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A381668 Ternary modular Gray code for n written in base 3.

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