A102393 - OEIS

%I #13 Aug 02 2020 04:12:27

%S 1,0,0,4,0,6,7,0,0,10,11,0,13,0,0,16,0,18,19,0,21,0,0,24,25,0,0,28,0,

%T 30,31,0,0,34,35,0,37,0,0,40,41,0,0,44,0,46,47,0,49,0,0,52,0,54,55,0,

%U 0,58,59,0,61,0,0,64,0,66,67,0,69,0,0,72,73,0,0,76,0,78,79,0,81,0,0,84,0,86

%N A wicked evil sequence.

%C Elements of A026147 (evil numbers plus one) appear at positions indexed by the evil numbers A001969, 0 otherwise. A000027(n) = A102393(n) + A102394(n).

%C The following sequences all appear to have the same parity: A003071, A029886, A061297, A092524, A093431, A102393, A104258, A122248, A128975. - _Jeremy Gardiner_, Dec 28 2008

%H Tanya Khovanova, <a href="http://arxiv.org/abs/1410.2193">There are no coincidences</a>, arXiv preprint 1410.2193 [math.CO], 2014.

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

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

%t a[n_] := If[EvenQ @ DigitCount[n, 2, 1], n + 1, 0]; Array[a, 100, 0] (* _Amiram Eldar_, Aug 02 2020 *)

%Y Cf. A000027, A000120, A001969, A010060, A026147, A102391, A102393, A102394.

%Y Cf. A003071, A029886, A061297, A092524, A093431, A104258, A122248, A128975.

%K easy,nonn

%O 0,4

%A _Paul Barry_, Jan 06 2005