|
| |
|
|
A048716
|
|
Numbers n such that binary expansion matches ((0)*00(1?)1)*(0*).
|
|
9
|
|
|
|
0, 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 19, 24, 25, 32, 33, 34, 35, 36, 38, 48, 49, 50, 51, 64, 65, 66, 67, 68, 70, 72, 73, 76, 96, 97, 98, 99, 100, 102, 128, 129, 130, 131, 132, 134, 136, 137, 140, 144, 145, 146, 147, 152, 153, 192, 193, 194, 195, 196, 198, 200, 201
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
If bit i is 1, then bits i+-2 must be 0. All terms satisfy A048725(n) = 5*n.
It appears that n is in the sequence if and only if C(5n,n) is odd (cf. A003714). - Benoit Cloitre, Mar 09 2003
Yes, as remarked in A048715, "This is easily proved using the well-known result that the multiplicity with which a prime p divides C(n+m,n) is the number of carries when adding n+m in base p." - Jason Kimberley, Dec 21 2011
A116361(a(n)) <= 2. - Reinhard Zumkeller, Feb 04 2006
|
|
|
LINKS
|
Table of n, a(n) for n=1..63.
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
|
|
|
MATHEMATICA
|
Reap[Do[If[OddQ[Binomial[5n, n]], Sow[n]], {n, 0, 400}]][[2, 1]]
|
|
|
PROG
|
(PARI) is(n)=!bitand(n, n>>2) \\ Charles R Greathouse IV, Oct 03 2016
|
|
|
CROSSREFS
|
Superset of A048715 and A048719. Cf. A048729, A003714, A115845, A115847, A116360.
Sequence in context: A002348 A019469 A081491 * A010434 A074230 A064438
Adjacent sequences: A048713 A048714 A048715 * A048717 A048718 A048719
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Antti Karttunen, 30.3.1999
|
|
|
STATUS
|
approved
|
| |
|
|
