A108882 Period doubling sequence starting with '1 0 1'.

1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1

Offset: 1

Author

Alexandre Losev, Jul 14 2005

Keywords

• easy
• nonn

Comments

Start with S = 1,0,1; replace S by SS and complement the last bit; iterate.

Similar to A035263 but with a different start.

Crossrefs

Cf. A035263.

Programs

Mathematica

f[l_] := Block[{s = Flatten[{l, l}]}, s[[ -1]] = Mod[s[[ -1]] + 1, 2]; s]; Nest[f, {1, 0, 1}, 6] (* Robert G. Wilson v, Jul 16 2005 *)

Python

def f(l):
    s = l + l
    s[-1] = (s[-1] + 1) % 2
    return s
result = [1, 0, 1]
for _ in range(6):
    result = f(result)
print(result) # Robert C. Lyons, Jan 19 2025

Extensions

More terms from Robert G. Wilson v, Jul 16 2005