OFFSET
1
COMMENTS
Let u(n) = # 0's <= n and v(n) = # 1's <= n. Let r = (7+sqrt(17))/4 and s = (-1+sqrt(17))/2, so that 1/r + 1/s = 1. Conjecture: -1 < n*r - u(n) < 3 and -1 < n*s - v(n) < 2 for n >= 1.
LINKS
EXAMPLE
1 -> 10101 -> 10101110101110101 -> ...
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 0, 1, 0, 1}}] &, {0}, 10] (* A283966 *)
Flatten[Position[s, 0]] (* A283967 *)
Flatten[Position[s, 1]] (* A284015 *)
SubstitutionSystem[{0->{1}, 1->{1, 0, 1, 0, 1}}, {1}, {5}][[1]] (* Harvey P. Dale, Mar 24 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 26 2017
STATUS
approved