OFFSET
1,1
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...
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
Clark Kimberling, Dec 19 2020
STATUS
approved