[go: up one dir, main page]

login
Search: a115846 -id:a115846
     Sort: relevance | references | number | modified | created      Format: long | short | data
Numbers n such that there is no bit position where the binary expansions of n and 8n are both 1.
+10
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
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
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.
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

Search completed in 0.024 seconds