VOOZH about

URL: https://oeis.org/A379183

⇱ A379183 - OEIS

login
A379183
a(1)=0, a(2)=a(3)=1; a(n) = n - a(a(n-2)) for n>3.
2
0, 1, 1, 4, 5, 2, 2, 7, 8, 8, 4, 5, 9, 9, 7, 8, 15, 11, 12, 16, 16, 14, 15, 15, 18, 19, 16, 16, 21, 22, 15, 18, 26, 23, 16, 21, 29, 22, 18, 26, 30, 23, 21, 29, 29, 25, 26, 30, 30, 28, 29, 36, 32, 33, 37, 30, 28, 36, 43, 39, 40, 44, 37, 35, 36, 50, 46, 40, 44, 44, 42, 43, 50, 53, 47, 44
OFFSET
1,4
COMMENTS
For the interesting properties of this sequence and A379184, see the article "Finding missing gems amidst chaos".
FORMULA
a(n) ~ n/phi.
MAPLE
a:= proc(n) option remember; `if`(n<4, signum(n-1), n-a(a(n-2))) end:
seq(a(n), n=1..76); # Alois P. Heinz, Dec 21 2024
MATHEMATICA
Block[{a}, a[1]=0; a[2]=a[3]=1; a[n_]:=a[n]=n-a[a[n-2]]; a/@Range[50]]
PROG
(PARI)
a(n)={my(b); b=vector(n); for(n=1, n, b[n]=if(
n==1, 0, n==2, 1, n==3, 1, n-b[b[n-2]])); b[n]}
(Go)
func a(n int) int {
b := make([]int, n+1);
copy(b, []int{0, 0, 1, 1});
for i:=4; i < n+1; i++ {
b[i] = i-b[b[i-2]];
};
return b[n]
}
CROSSREFS
KEYWORD
nonn
AUTHOR
Bradley Klee, Dec 17 2024
STATUS
approved