A078176 Numbers given by the Rule 225 Cellular Automaton.

7, 11, 15, 19, 23, 27, 63, 67, 71, 75, 79, 83, 87, 91, 127, 131, 135, 139, 143, 147, 151, 155, 191, 195, 455, 715, 975, 1235, 1495, 1755, 4095, 4099, 4103, 4107, 4111, 4115, 4119, 4123, 4159, 4163, 4167, 4171, 4175, 4179, 4183, 4187, 4223, 4227, 4231, 4235

Offset

1,1

Comments

Discovered by Stephen Wolfram in 1981.

Binary complement of A267843, the usual decimal representation of Rule 225: ON (black) cells are represented by 0 bits and OFF (white) cells by 1 bits here. The single start bit 0 is omitted. - Georg Fischer, Dec 19 2021

References

S. Wolfram, A New Kind of Science, p. 58.

Links

Table of n, a(n) for n=1..50.

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Formula

Binary Cellular Automaton. {1, 1, 1}, {1, 1, 0}, {1, 0, 1}, {0, 0, 1} produce 1.

a(n) = A267843(n) XOR (2^(2*n+1) - 1) for n >= 1. - Georg Fischer, Dec 19 2021

Mathematica

With[{k = Abs[Drop[CellularAutomaton[225, {{1}, 0}, 100], 1] - 1]}, Table[FromDigits[RotateLeft[k[[n]], n + 2], 2], {n, 1, Length[k]}]]

Crossrefs

Cf. A267843.

Sequence in context: A248630 A130569 A294294 * A097494 A037136 A023486

Adjacent sequences: A078173 A078174 A078175 * A078177 A078178 A078179

Keyword

nonn

Author

Ed Pegg Jr, Nov 20 2002

Status

approved