A102394 A wicked odious sequence.

0, 2, 3, 0, 5, 0, 0, 8, 9, 0, 0, 12, 0, 14, 15, 0, 17, 0, 0, 20, 0, 22, 23, 0, 0, 26, 27, 0, 29, 0, 0, 32, 33, 0, 0, 36, 0, 38, 39, 0, 0, 42, 43, 0, 45, 0, 0, 48, 0, 50, 51, 0, 53, 0, 0, 56, 57, 0, 0, 60, 0, 62, 63, 0, 65, 0, 0, 68, 0, 70, 71, 0, 0, 74, 75, 0, 77, 0, 0, 80, 0, 82, 83, 0, 85, 0

Offset: 0

Author

Paul Barry, Jan 06 2005

Keywords

• easy
• nonn

Comments

Odious numbers plus one (A000069(n)+1) appear at positions indexed by the odious numbers, 0 otherwise. A000027(n) = A102393(n) + A102394(n).

Crossrefs

Cf. A000027, A000069, A000120, A010060, A102392, A102393.

Programs

Mathematica

a[n_] := If[OddQ @ DigitCount[n, 2, 1], n + 1, 0]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2020 *)

Formula

a(n) = (n+1)(1-(-1)^A000120(n))/2.

a(n) = (n+1)(1-(-1)^A010060(n))/2.