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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 Michael S. Branicky, Table of n, a(n) for n = 0..10000 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 Cf. A267371, A267373. Sequence in context: A301750 A086676 A055804 * A369696 A355975 A327421 Adjacent sequences: A267369 A267370 A267371 * A267373 A267374 A267375 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.)