A255817 Parity of A000788, which is the total number of ones in 0..n in binary.

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

Offset

0

Comments

a(n) is also the parity of A115384.

a(n) is also the base 2 version of the process described in A256379.

Links

Danny Rorabaugh, Table of n, a(n) for n = 0..10000

Jeffrey Shallit and Anatoly Zavyalov, Transduction of Automatic Sequences and Applications, arXiv:2303.15203 [cs.FL], 2023, see p. 5.

Formula

a(n) = A000788(n) mod 2 = (Sum_{k=0..n} A000120(k)) mod 2.

a(n) = A115384(n) mod 2 = (Sum_{k=0..n} A010060(k)) mod 2.

Example

a(3) = 0, because there are an even number of ones in [0,1,10,11].
a(5) = 1, because there are an odd number of ones in [0,1,10,11,100,101].

Mathematica

Boole @* OddQ /@ Accumulate@ Array[DigitCount[#, 2, 1] &, 120, 0] (* Michael De Vlieger, Mar 29 2023 *)

Prog

(Sage)
def A255817(N):
    A = [0]
    for n in range(1, N+1):
        n2 = bin(n)[2:]
        A.append(mod(A[-1]+sum([int(n2[j]) for j in range(len(n2))]), 2))
    return A
A255817(120)
(Python)
def A255817(n): return ((n>>1)&1)^(n&1|((n+1).bit_count()&1^1)) # Chai Wah Wu, Mar 01 2023

Crossrefs

Cf. A000120, A000788, A010060, A115384.

Sequence in context: A138710 A356556 A330037 * A071674 A179829 A172486

Adjacent sequences: A255814 A255815 A255816 * A255818 A255819 A255820

Keyword

nonn,easy

Author

Danny Rorabaugh, Apr 01 2015

Status

approved