

A115845


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


7



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, 56, 64, 65, 66, 67, 68, 69, 70, 71, 80, 81, 84, 85, 96, 97, 98, 99, 112, 113, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 140, 142, 160, 161, 162, 163, 168, 170, 192
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OFFSET

1,3


COMMENTS

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).
Equivalently, numbers n such that the binomial coefficient C(9n,n) (A169958) is odd.  Zak Seidov, Aug 06 2010
The equivalence of these three definitions follows from Lucas's theorem on binomial coefficients.  N. J. A. Sloane, Sep 01 2010
Clearly all numbers k*2^i for 1 <= k <= 7 have this property.  N. J. A. Sloane, Sep 01 2010


LINKS



FORMULA



MATHEMATICA

Reap[Do[If[OddQ[Binomial[9n, n]], Sow[n]], {n, 0, 400}]][[2, 1]] (* Zak Seidov, Aug 06 2010 *)


PROG



CROSSREFS

A115846 shows this sequence in binary.


KEYWORD

nonn


AUTHOR



EXTENSIONS

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


STATUS

approved



