A267372 Lengths of iterates in A267371.

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

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