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A267373 Lengths of prefixes occurring in the sequence of iterates defining A267371. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
First differences of A267372.
LINKS
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
Sequence in context: A305924 A328134 A218785 * A075061 A032876 A032843
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Jan 13 2016
STATUS
approved

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Last modified June 25 01:31 EDT 2024. Contains 373691 sequences. (Running on oeis4.)