A078176 - OEIS

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

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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.