A285431 Fixed point of the morphism 0->11, 1-> 110.

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

Offset

1

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

J. Shallit, Proof of Irvine's conjecture via mechanized guessing, arXiv preprint arXiv:2310.14252 [math.CO], October 22 2023.

Index entries for sequences that are fixed points of mappings

Example

0 -> 11 -> 110110- -> 1101101111011011  -> 11011011110110111101101101101111011011110110 ->

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {1, 1, 0}}] &, {0}, 13] (* A285431 *)
Flatten[Position[s, 0]]  (* A026368 *)
Flatten[Position[s, 1]]  (* A026367 *)

Prog

(Python)
from itertools import islice
def A285431_gen(): # generator of terms
    a, l = [1, 1], 0
    while True:
        yield from a[l:]
        c = sum(([1, 1, 0] if d else [1, 1] for d in a), start=[])
        l, a = len(a), c
A285431_list = list(islice(A285431_gen(), 30)) # Chai Wah Wu, Nov 30 2023

Crossrefs

Cf. A026367, A026368.

Sequence in context: A080764 A291137 A285421 * A267621 A374039 A014114

Adjacent sequences: A285428 A285429 A285430 * A285432 A285433 A285434

Keyword

nonn,easy

Author

Clark Kimberling, Apr 29 2017

Status

approved