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A356215
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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.
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2
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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
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OFFSET
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0,4
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COMMENTS
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This sequence is a variant of A352528; here the cellular automaton maps 2 cells into 1, there 3 cells into 1.
The binary digit of a(n) at place value 2^k is a function of the binary digits of n at place values 2^(k+1) and 2^k (and of (2*n) mod 256).
We use even elementary cellular automaton rules, so "00" will always evolve to "0", and the binary expansion of a(n) will have finitely many 1's and will be correctly defined.
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LINKS
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FORMULA
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a(2^k-1) = 2^k-1 for any k <> 2.
a(2^k) = 0 for any k > 1.
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EXAMPLE
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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.
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PROG
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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) }
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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