A249952 Rank of first single 1 in A000002 such that A249949 takes the value n.

7, 10, 55, 82, 307, 460, 23374, 35981, 53975, 80982, 832448, 3966372, 8440210, 27554261, 41331096, 90179771, 135268972, 595383340, 1221488589, 1832231329, 2748344566

Offset

1,1

Comments

It is not known if this sequence is defined for any n > 0; showing that it is would solve some of the problems posed by Clark Kimberling about the Kolakoski sequence A000002 (see the link), at least the 2nd and 3rd problems.

a(22) > 7.7*10^10, if exists. - Andrei Zabolotskii, Oct 06 2025

Links

Table of n, a(n) for n=1..21.

C. Kimberling, Integer Sequences and Arrays, Illustration of the Kolakoski sequence

Prog

(Rust)
const TWO: u8 = u8::MAX;
const SIZE: usize = 2<<30;
fn main() {
  let mut kol: Vec<u8> = vec![0; SIZE];
  kol[1] = TWO;
  let mut j = 1;
  let mut n = 1;
  for i in 1..SIZE {
    if kol[i] == TWO {
      if i % 2 == 1 && j+1 < SIZE {
        kol[j] = TWO;
        kol[j+1] = TWO;
      }
    } else {
      if i % 2 == 1 {
        if j < SIZE { kol[j] = TWO; }
      } else {
        let c = kol[i] + 1;
        if j < SIZE { kol[j] = c; }
        if c == n {
          println!("{}", j+1);
          n += 1;
        }
      }
    }
    j += if kol[i] == TWO {2} else {1};
  }
} // Andrei Zabolotskii, Oct 06 2025

Crossrefs

Cf. A000002, A249507, A249508, A249942, A249948, A249949.

Sequence in context: A045770 A025632 A038276 * A187999 A097187 A115904

Adjacent sequences: A249949 A249950 A249951 * A249953 A249954 A249955

Keyword

nonn,more

Author

Jean-Christophe Hervé, Nov 09 2014

Extensions

a(16)-a(21) from Andrei Zabolotskii, Oct 06 2025

Status

approved