A182582 a(n) = (A096268(n-1) + A182581(n)) mod 2.

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

Offset

1

Comments

Parity of A169611 (the sum of the 2-adic and 3-adic valuations of n). - Antti Karttunen, Jul 02 2024

Links

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

Dimitri Hendriks, Frits G. W. Dannenberg, Jorg Endrullis, Mark Dow and Jan Willem Klop, Arithmetic Self-Similarity of Infinite Sequences, arXiv preprint 1201.3786 [math.CO], 2012. See Table 1.

Index entries for characteristic functions.

Formula

a(n) = A000035(A169611(n)) = A000035(A007814(n)+A007949(n)). - Antti Karttunen, Jul 02 2024

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 5/12. - Amiram Eldar, Jul 03 2024

Mathematica

A096268 = Join[{{0}}, SubstitutionSystem[{0 -> {0, 1}, 1 -> {0, 0}}, {1}, 6]] // Flatten;
A182581 = Mod[IntegerExponent[Range[Length[A096268]], 3], 2];
Mod[A096268 + A182581, 2] (* Jean-François Alcover, Feb 13 2019 *)
a[n_] := Mod[Plus @@ IntegerExponent[n, {2, 3}], 2]; Array[a, 100] (* Amiram Eldar, Jul 03 2024 *)

Prog

(PARI) A182582(n) = ((valuation(n, 2)+valuation(n, 3))%2); \\ Antti Karttunen, Jul 02 2024

Crossrefs

Characteristic function of A325424, whose complement A036668 gives the indices of 0's.

Cf. A000035, A007814, A007949, A096268, A169611, A182581, A373136, A373156.

Sequence in context: A189816 A342000 A194685 * A125720 A095130 A284789

Adjacent sequences: A182579 A182580 A182581 * A182583 A182584 A182585

Keyword

nonn,easy

Author

N. J. A. Sloane, May 06 2012

Extensions

Indexing of A096268 corrected in the definition, to match with the data - Antti Karttunen, Jul 02 2024

Status

approved