

A092246


Odd "odious" numbers (A000069).


23



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
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OFFSET

1,2


COMMENTS

In other words, numbers having a binary representation ending in 1, and an odd number of 1s overall. It follows that by decrementing an odd odius 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) = A026147th odd numbers, where A026147 = (1, 4, 6, 7, 10, 11,...); e.g.
1...2,..3,..4,..5,...6,...7,...8,...9,..10,..11,..12,..13,...
1,..3,..5,..7,..9,..11,..13,..15,..17,..19,..21,..23,..25,...
1...........7,......11,..13,............19,..21,.......25,...; etc... (End)
Numbers m, such that when mergesorting 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

T. D. Noe, Table of n, a(n) for n = 1..1000
Index entries for sequences related to binary expansion of n
Index entries for sequences related to sorting


FORMULA

a(n)=4*n+2*A010060(n1)3; a(n) = 2*A001969(n1)+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]]]&] (* JeanFrançois Alcover, Mar 15 2016 *)


PROG

(PARI) is(n)=n%2&&hammingweight(n)%2 \\ Charles R Greathouse IV, Mar 21 2013
(PARI) a(n)=4*nif(hammingweight(n1)%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


CROSSREFS

Cf. A129771, A026147.
Cf. A230709 (complement).
Cf. A268717, A268718, A268673.
Sequence in context: A257125 A064149 A046289 * A084468 A292315 A274915
Adjacent sequences: A092243 A092244 A092245 * A092247 A092248 A092249


KEYWORD

nonn,easy


AUTHOR

Benoit Cloitre, Feb 23 2004


STATUS

approved



