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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 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

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