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A092246 Odd "odious" numbers (A000069). 24
1, 7, 11, 13, 19, 21, 25, 31, 35, 37, 41, 47, 49, 55, 59, 61, 67, 69, 73, 79, 81, 87, 91, 93, 97, 103, 107, 109, 115, 117, 121, 127, 131, 133, 137, 143, 145, 151, 155, 157, 161, 167, 171, 173, 179, 181, 185, 191, 193, 199, 203, 205, 211, 213, 217, 223, 227, 229, 233 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
In other words, numbers having a binary representation ending in 1, and an odd number of 1's overall. It follows that by decrementing an odd odious number, one gets an even evil number (A125592). - Ralf Stephan, Aug 27 2013
The members of the sequence may be called primitive odious numbers because every odious number is a power of 2 times one of these numbers. Note that the difference between consecutive terms is either 2, 4, or 6. - T. D. Noe, Jun 06 2007
From Gary W. Adamson, Apr 06 2010: (Start)
a(n) = A026147(n)-th odd number, where A026147 = (1, 4, 6, 7, 10, 11, ...); e.g.,
n: 1 2 3 4 5 6 7 8 9 10 11
n-th odd: 1 3 5 7 9 11 13 15 17 19 21
a(n): 1 7 11 13 19 21
etc. (End)
Numbers m, such that when merge-sorting lists of length m, the maximal number of comparisons is even: A003071(a(n)) = A230720(n). - Reinhard Zumkeller, Oct 28 2013
Fixed points of permutation pair A268717/A268718. - Antti Karttunen, Feb 29 2016
LINKS
FORMULA
a(n) = 4*n + 2*A010060(n-1) - 3;
a(n) = 2*A001969(n-1) + 1.
MATHEMATICA
Table[If[n < 1, 0, 2 n - 1 - Mod[First@ DigitCount[n - 1, 2], 2]], {n, 120}] /. n_ /; EvenQ@ n -> Nothing (* Michael De Vlieger, Feb 29 2016 *)
Select[Range[1, 1001, 2], OddQ[Total[IntegerDigits[#, 2]]]&] (* Jean-François Alcover, Mar 15 2016 *)
PROG
(PARI) is(n)=n%2&&hammingweight(n)%2 \\ Charles R Greathouse IV, Mar 21 2013
(PARI) a(n)=4*n-if(hammingweight(n-1)%2, 1, 3) \\ Charles R Greathouse IV, Mar 22 2013
(Haskell)
a092246 n = a092246_list !! (n - 1)
a092246_list = filter odd a000069_list
-- Reinhard Zumkeller, Oct 28 2013
(Python)
def A092246(n): return (n<<2)-(1 if (n-1).bit_count()&1 else 3) # Chai Wah Wu, Mar 03 2023
CROSSREFS
Cf. A230709 (complement).
Sequence in context: A257125 A064149 A046289 * A084468 A292315 A372781
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Feb 23 2004
STATUS
approved

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Last modified July 15 16:36 EDT 2024. Contains 374333 sequences. (Running on oeis4.)