A356215 The binary expansion of a(n) is obtained by applying the elementary cellular automaton with rule (2*n) mod 16 to the binary expansion of n.
0, 1, 1, 2, 0, 5, 3, 7, 0, 9, 5, 14, 4, 13, 7, 15, 0, 17, 9, 26, 0, 21, 11, 31, 0, 17, 5, 22, 12, 29, 15, 31, 0, 33, 17, 50, 0, 37, 19, 55, 0, 41, 21, 62, 4, 45, 23, 63, 0, 33, 9, 42, 16, 53, 27, 63, 0, 33, 5, 38, 28, 61, 31, 63, 0, 65, 33, 98, 0, 69, 35, 103
Offset: 0
Examples
For n = 11:
- we use rule 22 mod 16 = 6,
- the binary expansion of 6 is "0110", so we apply the following evolutions:
11 10 01 00
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v v v v
0 1 1 0
- the binary expansion of 11 (with a leading 0's) is "...01011",
- the binary digit of a(11) at place value 2^0 is 0 (from "11"),
- the binary digit of a(11) at place value 2^1 is 1 (from "01"),
- the binary digit of a(11) at place value 2^2 is 1 (from "10"),
- the binary digit of a(11) at place value 2^3 is 1 (from "01"),
- the binary digit of a(11) at other places is 0 (from "00"),
- so the binary expansion of a(11) is "1110",
- and a(11) = 14.
Links
Programs
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PARI
a(n) = { my (v=0, m=n); for (k=0, oo, if (m==0, return (v), bittest(2*n, m%4), v+=2^k); m\=2) }
Formula
a(2^k-1) = 2^k-1 for any k <> 2.
a(2^k) = 0 for any k > 1.
Comments