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A254377
Characteristic function of A230709: a(n) = 1 if n is either evil (A001969) or even odious (A128309), otherwise 0 (when n is odd odious).
3
1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1
OFFSET
0
COMMENTS
A228495 is the characteristic function of the odd odious numbers (A092246).
A230709 is the union of even odious (A128309) and evil (A001969) numbers.
This sequence equals the parity of A003071, A093431, A122248, and A175186 (allowing for offsets).
Run lengths are given by A254378.
LINKS
Tanya Khovanova, There are no coincidences, arXiv preprint 1410.2193 [math.CO], 2014.
FORMULA
a(n) = 1-A228495(n).
MATHEMATICA
a[n_] := If[!OddQ[n] || !OddQ[DigitCount[n, 2, 1]], 1, 0]; Array[a, 100, 0] (* Amiram Eldar, Aug 06 2023 *)
PROG
(PARI) A254377(n) = !((n%2)&&(hammingweight(n)%2)); \\ Antti Karttunen, Sep 27 2019
(Python)
def A254377(n): return n.bit_count()&1&n^1 # Chai Wah Wu, Mar 09 2023
KEYWORD
nonn,base
AUTHOR
Jeremy Gardiner, Jan 29 2015
EXTENSIONS
Secondary part of name added by Antti Karttunen, Sep 27 2019
STATUS
approved