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

1,2

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

Formula

Other identities. For all n >= 1:

A269169(a(n)) = n.

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 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A269164 (MATCHING-POS 1 1 (lambda (n) (zero? (A269162 n)))))

Crossrefs

Complement: A269163.

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

Cf. A269169 (left inverse).

Cf. A269160, A269168.

Sequence in context: A163101 A157465 A257247 * A356899 A230780 A302540

Adjacent sequences: A269161 A269162 A269163 * A269165 A269166 A269167

Keyword

nonn

Author

Antti Karttunen, Feb 20 2016

Status

approved