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Revision History for A269168

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A269168

Rule 30 binary tree permutation: a(1) = 1, a(2n) = A269160(a(n)), a(2n+1) = A269164(1+a(n)).
(history; published version)

#16 by Susanna Cuyler at Tue Dec 10 12:10:02 EST 2019

STATUS

proposed

approved

#15 by Antti Karttunen at Tue Dec 10 10:04:43 EST 2019

STATUS

editing

proposed

#14 by Antti Karttunen at Tue Dec 10 10:04:34 EST 2019

LINKS

Antti Karttunen, <a href="/A135141/a135141.pdf">Entanglement Permutations</a>, 2016-2017

KEYWORD

nonn,tabf,look

STATUS

approved

editing

#13 by N. J. A. Sloane at Tue Feb 23 13:42:58 EST 2016

STATUS

proposed

approved

#12 by Jean-François Alcover at Tue Feb 23 12:58:38 EST 2016

STATUS

editing

proposed

#11 by Jean-François Alcover at Tue Feb 23 12:57:55 EST 2016

MATHEMATICA

nmax = (* sequence length *) 100; terms (* from A269164 *) = 2000; Clear[a, f]; A269160[n_] := BitXor[n, BitOr[2 n, 4 n]]; f[max_] := f[max] = (s = Sort[Table[A269160[n], {n, 0, max}]]; Complement[Range[Last[s]], s][[1 ;; terms]]); f[terms]; f[max = 2 terms]; While[f[max] != f[max/2], max = 2 max]; A269164[n_Integer] := If[n > Length[f[max]], 0, f[max][[n]]]; a[1] = 1; a[n_] := a[n] = If[EvenQ[n], A269160[a[n/2]], A269164[1 + a[(n - 1)/2]]]; A269168 = Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Feb 23 2016 *)

STATUS

proposed

editing

#10 by Antti Karttunen at Tue Feb 23 12:12:18 EST 2016

STATUS

editing

proposed

#9 by Antti Karttunen at Tue Feb 23 12:05:48 EST 2016

COMMENTS

Each maximal leftward branch (e.g. 1, 7, 25, ... (= A110240) or 9, 63, 193, ... or 2, 14, 50, ...) gives a history trajectory of Rule 30 cellular automaton starting from a particular "seed configuration" which are given in A269164.

#8 by Antti Karttunen at Tue Feb 23 12:03:53 EST 2016

COMMENTS

etc.

Each maximal leftward branch (e.g. 9, 63, 193, ... or 2, 14, 50, ...) gives a history of Rule 30 cellular automaton starting from a particular "seed configuration" which are given in A269164.

STATUS

proposed

editing

#7 by Antti Karttunen at Sun Feb 21 23:38:41 EST 2016

STATUS

editing

proposed