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A115845 Numbers n such that there is no bit position where the binary expansions of n and 8n are both 1. 6
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 (list; graph; refs; listen; history; text; internal format)
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

A116361(a(n)) <= 3. - Reinhard Zumkeller, Feb 04 2006

LINKS

N. J. A. Sloane and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Index entries for sequences defined by congruent products between domains N and GF(2)[X]

Index entries for sequences defined by congruent products under XOR

FORMULA

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

MATHEMATICA

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

PROG

(PARI) is(n)=!bitand(n, n<<3) \\ Charles R Greathouse IV, Sep 23 2012

CROSSREFS

A115846 shows this sequence in binary.

A033052 is a subsequence.

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

Sequence in context: A178878 A175326 A018676 * A026507 A079645 A032958

Adjacent sequences:  A115842 A115843 A115844 * A115846 A115847 A115848

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 01 2006

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

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Last modified September 22 00:25 EDT 2017. Contains 292326 sequences.