A267372 - OEIS

%I #22 Mar 24 2024 07:38:27

%S 2,3,5,8,12,19,27,36,49,63,78,94,113,133,165,198,235,273,312,352,395,

%T 439,484,533,583,648,714,781,851,922,994,1070,1147,1225,1304,1399,

%U 1495,1592,1690,1791,1893,1996,2103,2211,2320,2430,2543,2657,2791,2926,3062,3199,3339,3480,3622,3768,3915,4063,4212,4364

%N Lengths of iterates in A267371.

%H Michael S. Branicky, <a href="/A267372/b267372.txt">Table of n, a(n) for n = 0..10000</a>

%e 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.

%t (* Function preLo[] is defined in A267371 *)

%t a267372[n_] := Map[StringLength[Last[#]]&, NestList[{preLo[#], StringJoin[#[[2]], StringTake[#[[2]], preLo[#]]]}&, {1, "01"}, n]]

%t a267372[59] (* _Hartmut F. W. Hoft_, Mar 22 2024 *)

%o (Python)

%o from itertools import count, islice

%o def agen(): # generator of terms

%o     astr, k, mink = "01", 2, 1

%o     while True:

%o         yield len(astr)

%o         for k in range(mink, len(astr)+1):

%o             if astr[1:].count(astr[:k]) == 0:

%o                 break

%o         mink = max(mink, k)

%o         astr += astr[:k]

%o print(list(islice(agen(), 60))) # _Michael S. Branicky_, Mar 23 2024

%Y Cf. A267371, A267373.

%K nonn

%O 0,1

%A _Jeffrey Shallit_, Jan 13 2016