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A352528
The binary expansion of a(n) is obtained by applying the elementary cellular automaton with rule (2*n) mod 256 to the binary expansion of n.
3
0, 1, 1, 2, 0, 4, 2, 6, 2, 11, 5, 12, 5, 12, 4, 12, 0, 17, 9, 26, 4, 21, 14, 30, 2, 19, 3, 18, 9, 25, 8, 24, 0, 33, 17, 50, 0, 36, 19, 54, 2, 35, 21, 52, 7, 38, 21, 52, 8, 41, 9, 42, 28, 61, 31, 62, 6, 39, 7, 38, 19, 51, 17, 48, 0, 65, 33, 98, 0, 68, 34, 103
OFFSET
0,4
COMMENTS
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+2), 2^(k+1) and 2^k (and of (2*n) mod 256).
We use even elementary cellular automaton rules, so "000" will always evolve to "0", and the binary expansion of a(n) will have finitely many 1's and will be correctly defined.
EXAMPLE
For n = 13:
- we apply rule 26,
- the binary expansion of 26 being "00011010", we apply the following evolutions:
111 110 101 100 011 010 001 000
0 0 0 1 1 0 1 0
- the binary expansion of 13 (with leading zeros) is "...0001101",
- the binary digit of a(13) at place value 2^0 is 0 (from "101"),
- the binary digit of a(13) at place value 2^1 is 0 (from "110"),
- the binary digit of a(13) at place value 2^2 is 1 (from "011"),
- the binary digit of a(13) at place value 2^3 is 1 (from "001"),
- the other binary digits of a(13) are 0 (from "000"),
- so the binary expansion of a(13) is "1100",
- so a(13) = 12.
PROG
(PARI) a(n) = { my (v=0, m=n); for (k=0, oo, if (m==0, return (v), bittest(2*n, m%8), v+=2^k); m\=2) }
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 19 2022
STATUS
approved