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%I A115845 #24 Feb 13 2015 09:08:21
%S A115845 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 A115845 56,64,65,66,67,68,69,70,71,80,81,84,85,96,97,98,99,112,113,128,129,
%U A115845 130,131,132,133,134,135,136,138,140,142,160,161,162,163,168,170,192
%N A115845 Numbers n such that there is no bit position where the binary expansions of n and 8n are both 1.
%C A115845 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 A115845 Equivalently, numbers n such that the binomial coefficient C(9n,n) (A169958) is odd. - _Zak Seidov_, Aug 06 2010
%C A115845 The equivalence of these three definitions follows from Lucas's theorem on binomial coefficients. - _N. J. A. Sloane_, Sep 01 2010
%C A115845 Clearly all numbers k*2^i for 1 <= k <= 7 have this property. - _N. J. A. Sloane_, Sep 01 2010
%C A115845 A116361(a(n)) <= 3. - _Reinhard Zumkeller_, Feb 04 2006
%H A115845 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 A115845 <a href="/index/Con#CongruCrossDomain">Index entries for sequences defined by congruent products between domains N and GF(2)[X]</a>
%H A115845 <a href="/index/Con#CongruXOR">Index entries for sequences defined by congruent products under XOR</a>
%F A115845 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 A115845 Reap[Do[If[OddQ[Binomial[9n,n]],Sow[n]],{n,0,400}]][[2,1]] (* _Zak Seidov_, Aug 06 2010 *)
%o A115845 (PARI) is(n)=!bitand(n,n<<3) \\ _Charles R Greathouse IV_, Sep 23 2012
%Y A115845 A115846 shows this sequence in binary.
%Y A115845 A033052 is a subsequence.
%Y A115845 Cf. A003714, A048716, A115847, A116360, A005809, A003714, A048716, A048715.
%K A115845 nonn
%O A115845 1,3
%A A115845 _Antti Karttunen_, Feb 01 2006
%E A115845 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

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