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A267372 Lengths of iterates in A267371. 3
2, 3, 5, 8, 12, 19, 27, 36, 49, 63, 78, 94, 113, 133, 165, 198, 235, 273, 312, 352, 395, 439, 484, 533, 583, 648, 714, 781, 851, 922, 994, 1070, 1147, 1225, 1304, 1399, 1495, 1592, 1690, 1791, 1893, 1996, 2103, 2211, 2320, 2430, 2543, 2657, 2791, 2926, 3062, 3199, 3339, 3480, 3622, 3768, 3915, 4063, 4212, 4364 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
EXAMPLE
Starting with 01 of length 2, we append the shortest prefix occurring only once to get 010 of length 3, then again to get 01001 of length 5, etc.
MATHEMATICA
(* Function preLo[] is defined in A267371 *)
a267372[n_] := Map[StringLength[Last[#]]&, NestList[{preLo[#], StringJoin[#[[2]], StringTake[#[[2]], preLo[#]]]}&, {1, "01"}, n]]
a267372[59] (* 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:
yield len(astr)
for k in range(mink, len(astr)+1):
if astr[1:].count(astr[:k]) == 0:
break
mink = max(mink, k)
astr += astr[:k]
print(list(islice(agen(), 60))) # Michael S. Branicky, Mar 23 2024
CROSSREFS
Sequence in context: A301750 A086676 A055804 * A369696 A355975 A327421
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Jan 13 2016
STATUS
approved

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Last modified July 23 10:38 EDT 2024. Contains 374547 sequences. (Running on oeis4.)