%I #24 Feb 13 2015 09:08:21

%S 0,1,2,3,4,5,6,7,8,10,12,14,16,17,20,21,24,28,32,33,34,35,40,42,48,49,

%T 56,64,65,66,67,68,69,70,71,80,81,84,85,96,97,98,99,112,113,128,129,

%U 130,131,132,133,134,135,136,138,140,142,160,161,162,163,168,170,192

%N Numbers n such that there is no bit position where the binary expansions of n and 8n are both 1.

%C Equivalently, numbers n such that 9*n = 9 X n, i.e., 8*n XOR n = 9*n. Here * stands for ordinary multiplication and X means carryless (GF(2)[X]) multiplication (A048720).

%C Equivalently, numbers n such that the binomial coefficient C(9n,n) (A169958) is odd. - _Zak Seidov_, Aug 06 2010

%C The equivalence of these three definitions follows from Lucas's theorem on binomial coefficients. - _N. J. A. Sloane_, Sep 01 2010

%C Clearly all numbers k*2^i for 1 <= k <= 7 have this property. - _N. J. A. Sloane_, Sep 01 2010

%C A116361(a(n)) <= 3. - _Reinhard Zumkeller_, Feb 04 2006

%H N. J. A. Sloane and Charles R Greathouse IV, <a href="/A115845/b115845.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Con#CongruCrossDomain">Index entries for sequences defined by congruent products between domains N and GF(2)[X]</a>

%H <a href="/index/Con#CongruXOR">Index entries for sequences defined by congruent products under XOR</a>

%F a(n)/n^k is bounded (but does not tend to a limit), where k = 1.44... = A104287. - _Charles R Greathouse IV_, Sep 23 2012

%t Reap[Do[If[OddQ[Binomial[9n,n]],Sow[n]],{n,0,400}]][[2,1]] (* _Zak Seidov_, Aug 06 2010 *)

%o (PARI) is(n)=!bitand(n,n<<3) \\ _Charles R Greathouse IV_, Sep 23 2012

%Y A115846 shows this sequence in binary.

%Y A033052 is a subsequence.

%Y Cf. A003714, A048716, A115847, A116360, A005809, A003714, A048716, A048715.

%K nonn

%O 1,3

%A _Antti Karttunen_, Feb 01 2006

%E Edited with a new definition by _N. J. A. Sloane_, Sep 01 2010, merging this sequence with a sequence submitted by _Zak Seidov_, Aug 06 2010