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 A341256 Concatenation of all 01-words in the order induced by A004526; see Comments. 7
 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS Let s = (s(n)) be a strictly increasing sequence of positive integers with infinite complement, t = (t(n)). For n >=1, let s'(n) be the number of s(i) that are <= n-1 and let t'(n) be the number of t(i) that are <= n-1. Define w(1) = 0, w(t(1)) = 1, and w(n) = 0w(s'(n)) if n is in s, and w(n) = 1w(t'(n)) if n is in t. Then (w(n)) is the "s-induced ordering" of all 01-words. **** Guide to related sequences:    s       01-words ordered by s            positions of palindromes A092754    A076478 (lexicographic order)    A341257 A004526    A341256                          A341257 A000201    A341258                          A341333 A016777    A341334                          A342750 A001651    A342753                          A342790 A032766    A342910                          A344166 LINKS FORMULA To generate successive words w(n), if n is in s, spell w(n) as 0 suffixed by the first w(k) that does not already suffix a word beginning with 0; otherwise, spell w(n) as 1 suffixed by the first w(k) that does not already suffix a word beginning with 1. EXAMPLE The first 20 words: 0, 1, 00, 10, 01, 11, 000, 100, 010, 110, 001, 101, 011, 111, 0000, 1000, 0100, 1100, 0010, 1010. MATHEMATICA z = 80; s = Table[2 n - 1, {n, 1, z}]; (* A004526 *) t = Complement[Range[Max[s]], s]; (* A005843 *) s1[n_] := Length[Intersection[Range[n - 1], s]]; t1[n_] := n - 1 - s1[n]; (* A023416 *) w = {0}; w[t[]] = {1}; w[n_] := If[MemberQ[s, n], Join[{0}, w[s1[n]]], Join[{1}, w[t1[n]]]] tt = Table[w[n], {n, 1, z}]  (* 01-words, in order *) Flatten[tt] (* A341256 *) CROSSREFS Cf. A004526, A005843, A023416, A092754, A341257. Sequence in context: A051065 A091445 A091446 * A270742 A164349 A094186 Adjacent sequences:  A341253 A341254 A341255 * A341257 A341258 A341259 KEYWORD nonn AUTHOR Clark Kimberling, Mar 16 2021 STATUS approved

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Last modified September 24 12:38 EDT 2021. Contains 347642 sequences. (Running on oeis4.)