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A228495
Characteristic function of the odd odious numbers (A092246).
5
0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0
OFFSET
0,1
COMMENTS
The following sequences all appear to have the same parity: A003071, A029886, A061297, A092524, A093431, A102393, A104258, A122248, A128975. - Jeremy Gardiner, Dec 28 2008.
a(n+1) is the characteristic function of the even evil numbers (A125592). - Jeremy Gardiner, Feb 06 2015
FORMULA
a(2n) = 0, a(2n+1) = A092436(n).
a(n) = A000035(n) * A010060(n). - Antti Karttunen, Jan 12 2019
MATHEMATICA
a[n_] := If[OddQ[n] && OddQ[DigitCount[n, 2, 1]], 1, 0]; Array[a, 100, 0] (* Amiram Eldar, Aug 06 2023 *)
PROG
(PARI) a(n)=if(n%2==0, 0, subst(Pol(binary((n-1)/2)), x, 1)%2==0)
(PARI) A228495(n) = ((n%2)&&(hammingweight(n)%2)); \\ Antti Karttunen, Jan 12 2019
(Python)
def A228495(n): return n.bit_count()&1&n # Chai Wah Wu, Mar 03 2023
KEYWORD
nonn,base
AUTHOR
Ralf Stephan, Aug 23 2013
STATUS
approved