A379275 - OEIS

%I #18 Jan 04 2025 17:30:45

%S 0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,1,

%T 0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,

%U 0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0

%N a(n) = A163801(n) mod 2.

%C Using Go language code found under Links, a search up to 10^9 terms counts irreducible missing binary words of lengths L = 1..20 as follows: [0, 1, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]. Relative to A379184, fewer omissions appear earlier and at more than one length.

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

%H Brad Klee, <a href="https://community.wolfram.com/groups/-/m/t/3289552">Finding missing gems amidst chaos</a>, Wolfram Community, 2024.

%H Bradley Klee, <a href="/A379275/a379275.go.txt">Conjecture Certificate (Golang)</a>

%H Stephen Wolfram, <a href="https://writings.stephenwolfram.com/2024/09/nestedly-recursive-functions/">Nestedly Recursive Functions</a>, 2024.

%t Block[{a}, a[0]=0; a[1]=1; a[n_]:=a[n]=n-a[a[n-2]]; Mod[a/@Range[0,50],2]]

%o (PARI) a(n)={my(b); b=vector(n+1); for(k=0, n, b[k+1]=if(k==0, 0, k==1, 1, k-b[b[k-1]+1])); b[n+1]%2}

%o (Go)

%o func a(n int) int {

%o     b := make([]int, n+1);

%o     copy(b, []int{0, 1});

%o     for i:=2; i < n+1; i++ {

%o         b[i] = i-b[b[i-2]];

%o     };

%o     return b[n]%2

%o }

%Y Cf. A163801, A171587, A379184, A379274.

%K nonn

%O 0

%A _Bradley Klee_, Dec 19 2024