A267373 Lengths of prefixes occurring in the sequence of iterates defining A267371.

1, 2, 3, 4, 7, 8, 9, 13, 14, 15, 16, 19, 20, 32, 33, 37, 38, 39, 40, 43, 44, 45, 49, 50, 65, 66, 67, 70, 71, 72, 76, 77, 78, 79, 95, 96, 97, 98, 101, 102, 103, 107, 108, 109, 110, 113, 114, 134, 135, 136, 137, 140, 141, 142, 146, 147, 148, 149, 152, 153, 165, 166, 199, 200, 201, 202, 205, 206, 207

Offset

1,2

Comments

First differences of A267372.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

Starting with 01, we append the shortest prefix occurring only once to get 010.  This is of length 1.  Next, we append the shortest prefix occurring only once (01) to get 01001.  This is of length 2, and so forth.

Mathematica

(* Function preLo[] is defined in A267371 *)
a267373[n_] := Map[First, Rest[NestList[{preLo[#], StringJoin[#[[2]], StringTake[#[[2]], preLo[#]]]}&, {1, "01"}, n]]]
a267373[69] (* Hartmut F. W. Hoft, Mar 22 2024 *)

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    astr, k, mink = "01", 2, 1
    while True:
        for k in range(mink, len(astr)+1):
            if astr[1:].count(astr[:k]) == 0:
                break
        mink = max(mink, k)
        astr += astr[:k]
        yield k
print(list(islice(agen(), 69))) # Michael S. Branicky, Mar 23 2024

Crossrefs

Cf. A267371, A267372.

Sequence in context: A305924 A328134 A218785 * A075061 A032876 A032843

Adjacent sequences: A267370 A267371 A267372 * A267374 A267375 A267376

Keyword

nonn

Author

Jeffrey Shallit, Jan 13 2016

Status

approved