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 A339826 a(n) = least k such that the first n-block in A339825 occurs in A339824 beginning at the k-th term. 4
 2, 2, 3, 7, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence begins with 2 2's, 1 3, 7 7's, 6 11's, ... Conjecture: the sequence includes infinitely many distinct numbers, in which case, every finite block in A339825 occurs infinitely many times in A339824. LINKS Table of n, a(n) for n=1..67. EXAMPLE Let W denote the infinite Fibonacci word A003849. A339824 = even bisection of W: 001100110001000100011... A339825 = odd bisection of W: 100010001100110011000... Using offset 1 for A339825, block #1 of A339824 is 0, which first occurs in A339825 beginning at the 2nd term, so a(1) = 2; block #4 of A339824 is 0100, which first occurs in A339825 beginning at the 7th term, so a(4) = 7. MATHEMATICA r = (1 + Sqrt[5])/2; z = 3000; f[n_] := 2 - Floor[(n + 2) r] + Floor[(n + 1) r]; (*A003849*) u = Table[f[2 n], {n, 0, Floor[z/2]}]; (*A339824 *) v = Table[f[2 n + 1], {n, 0, Floor[z/2]}]; (*A339825 *) a[n_] := Select[Range[z], Take[u, n] == Take[v, {#, # + n - 1}] &, 1] Flatten[Table[a[n], {n, 1, 300}]] (*A339826 *) CROSSREFS Cf. A001622, A339051, A339052, A339824, A339825, A339827. Sequence in context: A002583 A068519 A342848 * A108041 A259254 A095017 Adjacent sequences: A339823 A339824 A339825 * A339827 A339828 A339829 KEYWORD nonn AUTHOR Clark Kimberling, Dec 19 2020 STATUS approved

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Last modified September 11 17:54 EDT 2024. Contains 375839 sequences. (Running on oeis4.)