This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A217262 #33 Jan 08 2024 22:42:40 %S A217262 0,1,2,1,0,3,0,1,2,1,0,1,4,1,0,1,2,1,0,3,0,1,2,1,0,1,2,5,2,1,0,1,2,1, %T A217262 0,3,0,1,2,1,0,1,4,1,0,1,2,1,0,3,0,1,2,1,0,1,2,3,6,3,2,1,0,1,2,1,0,3, %U A217262 0,1,2,1,0,1,4,1,0,1,2,1,0,3,0,1,2,1,0,1,2,5,2,1,0,1,2,1,0,3,0,1,2,1,0,1,4,1,0,1,2,1,0,3,0,1,2,1,0,1,2,3,4 %N A217262 Delta sequence for binary words in a minimal-change order (subset-lex Gray code). %C A217262 Positions of change with a certain Gray code (SL-Gray) for binary words (see example): to keep the sequence independent of the word length we start with the all-ones word, the sequence gives the following changes. The Gray code is cyclic, so first words skipped can (for fixed word length) be appended to the end. %C A217262 Alternatively, for words length n, start with the all-zeros word, use transitions (n-2), (n-1), (n-2), (n-3), (n-4), ..., 3, 2, 1, 0, followed by the terms of this sequence until all 2^n words have been visited (see rows 00..05 in the example). %C A217262 The subset-lex Gray code shown here can be obtained by a reflection process from the (reversed) subset-lexicographic order for binary words given in A108918. %C A217262 Research problem: Does a two-close Gray code exist for the binary words of length n for all n? One-close Gray codes for binary words exists for n<=6 but not for n=7 (and unlikely for any n>=8, see Fxtbook link). %C A217262 From _Joerg Arndt_, Apr 29 2014: (Start) %C A217262 Sequence can be obtained from A007814 by replacing 0 by 01210, 1 by 3, 2 by 141, 3 by 12521, 4 by 1236321, ..., n by 123..(n-1)(n+2)(n-1)..321. - _Joerg Arndt_, Apr 29 2014 %C A217262 The consecutive transitions are either one-close (abs(a(n)-a(n-1))=1, most of the time) or 3-close (abs(a(n)-a(n-1))=3): In the Gray code of the 2^n n-bit words all transitions are one-close but for 2^(n-2) - 2 transitions that are 3-close; The Gray codes for n<=3 have only one-close transitions. %C A217262 (End) %C A217262 The positions of 0's are twice the terms of A327492. - _Andrey Zabolotskiy_, Jan 06 2024 %H A217262 Joerg Arndt, <a href="/A217262/b217262.txt">Table of n, a(n) for n = 0..4095</a> %H A217262 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 20.3.2 "Adjacent changes (AC) Gray codes", p.400. %H A217262 Joerg Arndt, <a href="http://www.jjj.de/fxt/demo/seq/#A217262">C++ code to compute this sequence</a>. %H A217262 Joerg Arndt, <a href="http://arxiv.org/abs/1405.6503">Subset-lex: did we miss an order?</a>, arXiv:1405.6503 [math.CO], (26-May-2014) %e A217262 Example for word length 5: %e A217262 no: word transition %e A217262 00: ..... .1... 3 %e A217262 01: 1.... 1.... 4 %e A217262 02: 11... .1... 3 %e A217262 03: 111.. ..1.. 2 %e A217262 04: 1111. ...1. 1 %e A217262 05: 11111 ....1 0 <--= sequence starts %e A217262 06: 111.1 ...1. 1 %e A217262 07: 11..1 ..1.. 2 %e A217262 08: 11.11 ...1. 1 %e A217262 09: 11.1. ....1 0 %e A217262 10: 1..1. .1... 3 %e A217262 11: 1..11 ....1 0 %e A217262 12: 1...1 ...1. 1 %e A217262 13: 1.1.1 ..1.. 2 %e A217262 14: 1.111 ...1. 1 %e A217262 15: 1.11. ....1 0 %e A217262 16: 1.1.. ...1. 1 %e A217262 17: ..1.. 1.... 4 %e A217262 18: ..11. ...1. 1 %e A217262 19: ..111 ....1 0 %e A217262 20: ..1.1 ...1. 1 %e A217262 21: ....1 ..1.. 2 %e A217262 22: ...11 ...1. 1 %e A217262 23: ...1. ....1 0 %e A217262 24: .1.1. .1... 3 %e A217262 25: .1.11 ....1 0 %e A217262 26: .1..1 ...1. 1 %e A217262 27: .11.1 ..1.. 2 %e A217262 28: .1111 ...1. 1 %e A217262 29: .111. ....1 0 %e A217262 30: .11.. ...1. 1 %e A217262 31: .1... ..1.. 2 %e A217262 Append first few words to obtain Gray code for word length 5: %e A217262 00: ..... .1... %e A217262 01: 1.... 1.... %e A217262 02: 11... .1... %e A217262 03: 111.. ..1.. %e A217262 04: 1111. ...1. %Y A217262 Cf. A007814 (transitions for the binary reflected Gray code). %Y A217262 Cf. A108918. %K A217262 nonn %O A217262 0,3 %A A217262 _Joerg Arndt_, Sep 29 2012 %E A217262 Prepended a(0)=0, _Joerg Arndt_, Apr 29 2014