A379183 a(1)=0, a(2)=a(3)=1; a(n) = n - a(a(n-2)) for n>3.

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".

Links

Table of n, a(n) for n=1..76.

Brad Klee, Finding missing gems amidst chaos, Wolfram Community, 2024.

Bradley Klee, Script for generating plaintext call tree (BASH)

Bradley Klee, Script for generating plaintext call tree (Golang)

Bradley Klee, Call tree (Golang output)

Stephen Wolfram, Nestedly Recursive Functions, 2024.

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

Cf. A379184, A005206, A135414, A163801.

Sequence in context: A255701 A085548 A329957 * A074459 A371747 A155793

Adjacent sequences: A379180 A379181 A379182 * A379184 A379185 A379186

Keyword

nonn

Author

Bradley Klee, Dec 17 2024

Status

approved