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A182582
a(n) = (A096268(n-1) + A182581(n)) mod 2.
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
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.
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.
Sequence in context: A189816 A342000 A194685 * A125720 A095130 A284789
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