A289748 Thue-Morse constant converted to base -2.

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

Offset

1

Comments

Base -2 is also called negabinary. Interpreting the sequence as a binary number with the first '1' at place 2^0 gives 1.101111101110... which in decimal equals M = 1.745787366973...

Links

Table of n, a(n) for n=1..105.

Formula

M = Thue-Morse + 4/3 (conjectured).

Prog

(Python)
def N(x):
    return x + 0xAAAAAAAAAAAAAAAA ^ 0xAAAAAAAAAAAAAAAA
def parityOf(int_type):
    parity = 0
    while (int_type):
        parity = ~parity
        int_type = int_type & (int_type - 1)
    return(abs(parity))
A010060 = ""
for i in range(0, 40):
    A010060 = A010060 + str(parityOf(i))
A289748 = ", ".join(bin(N(int(A010060, 2))).replace("0b", ""))
print(A289748)

Crossrefs

Cf. A010060, A014571.

Sequence in context: A103583 A070178 A364250 * A127254 A188395 A266678

Adjacent sequences: A289745 A289746 A289747 * A289749 A289750 A289751

Keyword

nonn,easy,cons,base

Author

Gilian Breysens, Jul 11 2017

Status

approved