A379274 a(n) = A135414(n) mod 2.

1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0

Offset

1

Comments

Using Go language code found under Links, a search up to 10^9 terms counts irreducible missing words of length L = 1..20 as follows: [0, 0, 0, 4, 2, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0].

A missing word is said to be irreducible if none of its subwords are missing.

Relative to A379184, fewer omissions appear earlier and at more than one length.

Links

Table of n, a(n) for n=1..80.

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

Bradley Klee, Conjecture certificate (golang)

Stephen Wolfram, Nestedly Recursive Functions, 2024.

Mathematica

Block[{a}, a[1]= a[2]=1; a[n_]:=a[n]=n-a[a[n-2]]; Mod[a/@Range[50], 2]]

Prog

(PARI)
a(n) = my(g = quadgen(5)); (n\g + (n + 1)\g - (n + 3)\g)%2;
alist(len) = my(b=vector(len)); for(n=1, len, b[n]=if(n==1, 1, n==2, 1, n-b[b[n-2]])); b%2;
(Go)
func b(n int) []int {
    a := make([]int, n+1);
    copy(a, []int{0, 1, 1});
    for i:=3; i < n+1; i++ {
        a[i] = i-a[a[i-2]];
    };
    for i:=0; i < n+1; i++ {
        a[i] = a[i]%2;
    };
    return a[1:]
}

Crossrefs

Cf. A135414, A171587, A379184, A379275.

Sequence in context: A354918 A354108 A181101 * A321512 A373489 A297054

Adjacent sequences: A379269 A379270 A379273 * A379275 A379276 A379277

Keyword

nonn,easy,new

Author

Bradley Klee, Dec 19 2024

Status

approved