A339826 - OEIS

A339826

a(n) = least k such that the first n-block in A339825 occurs in A339824 beginning at the k-th term.

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

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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 *)