A359832 a(n) = 1 if the 2-adic valuation of n is either 0 or odd, otherwise 0.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Formula

Multiplicative with a(2^e) = 1 if e is odd, and 0 if e is even (and > 0), with a(p^e) = 1 for all odd primes p.

a(n) = 1 - A328981(n).

a(n) = A000035(n+A048675(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 5/6. - Amiram Eldar, Jan 24 2023

Mathematica

a[n_] := If[(e = IntegerExponent[n, 2]) == 0 || OddQ[e], 1, 0]; Array[a, 100] (* Amiram Eldar, Jan 24 2023 *)

Prog

(PARI) A359832(n) = (!(n=valuation(n, 2))||(n%2));
(PARI) A359832(n) = { my(f=factor(n)); prod(k=1, #f~, ((2!=f[k, 1]) || (f[k, 2]%2))); };
(Python)
def A359832(n): return (n&1)|((~n & n-1).bit_length()&1) # Chai Wah Wu, Jan 24 2023

Crossrefs

Characteristic function of A359794.

Cf. A000035, A007814, A048675, A328981 (one's complement), A359833 (Dirichlet inverse).

Sequence in context: A129564 A317193 A293163 * A267871 A329678 A359942

Adjacent sequences: A359829 A359830 A359831 * A359833 A359834 A359835

Keyword

nonn,mult

Author

Antti Karttunen, Jan 24 2023

Status

approved