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 A336168 Garel's separator length for position n of the Thue-Morse sequence (A010060). 0
 1, 1, 2, 3, 3, 2, 5, 4, 5, 4, 4, 4, 9, 8, 7, 6, 9, 8, 7, 6, 7, 6, 7, 6, 17, 16, 15, 14, 13, 12, 11, 10, 17, 16, 15, 14, 13, 12, 11, 10, 13, 12, 11, 10, 13, 12, 11, 10, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 33, 32, 31, 30, 29, 28, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The separator length at position n is the length of the shortest block beginning at that position that never appeared earlier in the sequence. LINKS E. Garel, Séparateurs dans les mots infinis engendrés par morphismes, Theor. Comput. Sci. 180 (1997), 81-113. FORMULA a(4*n+3) = 2*a(2*n) - 2*a(2*n+1) - 2*a(4*n) + a(4*n+1) + 2*a(4*n+2). a(8*n)   = -2*a(2*n) + 3*a(4*n). a(8*n+1) = -2*a(2*n) + 2*a(4*n) + a(4*n+1). a(8*n+2) = 2*a(n) - 4*a(2*n) + a(2*n+1) + a(4*n) + 2*a(4*n+1). a(8*n+4) = -2*a(2*n) + a(4*n) + 2*a(4*n+2). a(8*n+5) = -4*a(2*n) + 2*a(4*n) + 2*a(4*n+2). a(8*n+6) = 2*a(2*n) - 4*a(2*n+1) - 3*a(4*n) + 2*a(4*n+1) + 4*a(4*n+2). EXAMPLE The first 10 symbols of Thue-Morse are 011010011001.  We index it starting with index 0.  Then a(6) = 5, because a(6..9) = 0110 already appears, while a(6..10) = 01100 does not. CROSSREFS Cf. A010060. Sequence in context: A131899 A095174 A131307 * A091813 A238114 A291300 Adjacent sequences:  A336165 A336166 A336167 * A336169 A336170 A336171 KEYWORD nonn AUTHOR Jeffrey Shallit, Jul 10 2020 STATUS approved

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Last modified June 17 05:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)