login
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.
2
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
0,4
COMMENTS
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.
FORMULA
a(2^k-1) = 2^k-1 for any k <> 2.
a(2^k) = 0 for any k > 1.
EXAMPLE
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
| | | |
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.
PROG
(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) }
CROSSREFS
Sequence in context: A071782 A328495 A297024 * A107363 A154954 A095245
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jul 29 2022
STATUS
approved