OFFSET
0
COMMENTS
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.
A missing word is said to be irreducible if none of its subwords are missing.
LINKS
Brad Klee, Finding missing gems amidst chaos, Wolfram Community, 2024.
Bradley Klee, Conjecture Certificate (Golang)
Stephen Wolfram, Nestedly Recursive Functions, 2024.
FORMULA
a(n) = A363057(n+2) - 1. - Ruud H.G. van Tol, Jan 15 2026
MATHEMATICA
Block[{a}, a[0]=0; a[1]=1; a[n_]:=a[n]=n-a[a[n-2]]; Mod[a/@Range[0, 50], 2]]
PROG
(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}
(Go)
func a(n int) int {
b := make([]int, n+1);
copy(b, []int{0, 1});
for i:=2; i < n+1; i++ {
b[i] = i-b[b[i-2]];
};
return b[n]%2
}
CROSSREFS
KEYWORD
nonn
AUTHOR
Bradley Klee, Dec 19 2024
STATUS
approved
