

A339827


a(n) = least k such that the first nblock in A339824 occurs in A339825 beginning at the kth term.


3



3, 4, 4, 8, 8, 8, 8, 8, 8, 12, 12, 12, 12, 12, 12, 12, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46
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OFFSET

1,1


LINKS



EXAMPLE

The sequence begins with one 3, two 4's, six 8's, six 12's, ... Conjecture: the sequence includes infinitely many distinct numbers, in which case, every finite block in A339824 occurs infinitely many times in A339825.
Let W denote the infinite Fibonacci word A003849.
A339824 = even bisection of W: 001100110001000100011...
A339825 = odd bisection of W: 100010001100110011000...
Using offset 1 for A339824, block #1 of A339825 is 1, which first occurs in A339824 beginning at the 3rd term, so a(1) = 3;
block #4 of A339824 is 0011, which first occurs in A339824 beginning at the 8th term, so a(4) = 8.


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



KEYWORD

nonn


AUTHOR



STATUS

approved



