A230709 Union of even odious (cf. A128309) and evil numbers (cf. A001969).

0, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 42, 43, 44, 45, 46, 48, 50, 51, 52, 53, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 70, 71, 72, 74, 75, 76, 77, 78, 80, 82, 83, 84, 85, 86, 88

Offset: 1

Author

Reinhard Zumkeller, Oct 28 2013

Keywords

• nonn
• easy

Comments

Apart from initial zero: numbers m, such that when mergesorting lists of length m, the maximal number of comparisons is odd: A003071(a(n+1)) = A230721(n).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sorting

Crossrefs

Cf. A092246 (complement).

Programs

Haskell

a230709 n = a230709_list !! (n-1)
a230709_list = filter (\x -> a010060 x * x `mod` 2 == 0) [0..]

Mathematica

Complement[Range[0, m = 88], Select[Range[1, m, 2], OddQ[ Total[ IntegerDigits[#, 2]]]&]] (* Jean-François Alcover, Dec 15 2018 *)

PARI

is(n)=if(hammingweight(n)%2,n%2==0,1) \\ Charles R Greathouse IV, May 09 2016

Formula

A010060(a(n)) * a(n) mod 2 = 0.