A269164 Numbers not in range of A269160; indices of zeros in A269162 from n >= 1 onward.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96

Offset: 1

Author

Antti Karttunen, Feb 20 2016

Keywords

• nonn

Comments

Natural numbers n for which there does not exist any number k such that A269160(k) = n.

These are binary representations (shown in decimal) of Garden of Eden patterns in Wolfram's Rule 30 cellular automaton if infinite predecessors are forbidden.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12285
• Eric Weisstein's World of Mathematics, Rule 30
• Index entries for sequences related to cellular automata
• Index to Elementary Cellular Automata

Crossrefs

Complement: A269163.

Indices of zeros in A269162 and A269166 (after the initial zero).

Cf. A269169 (left inverse).

Cf. A269160, A269168.

Programs

Mathematica

terms = 100; Clear[f]; f[max_] := f[max] = (s = Sort[Table[BitXor[n, BitOr[2n, 4n]], {n, 0, max}]]; Complement[Range[Last[s]], s][[1 ;; terms ]]); f[terms]; f[max = 2 terms]; While[Print[max]; f[max] != f[max/2], max = 2 max]; A269164 = f[max] (* Jean-François Alcover, Feb 23 2016 *)

Formula

Other identities. For all n >= 1:

A269169(a(n)) = n.