|
|
A214218
|
|
List of words over {1,2} with equal numbers of 1's and 2's.
|
|
9
|
|
|
12, 21, 1122, 1212, 1221, 2112, 2121, 2211, 111222, 112122, 112212, 112221, 121122, 121212, 121221, 122112, 122121, 122211, 211122, 211212, 211221, 212112, 212121, 212211, 221112, 221121, 221211, 222111, 11112222, 11121222, 11122122, 11122212, 11122221
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Of course the empty word also has this property.
All of these, interpreted as decimal integers are divisible by 3, because each pair of "1" and "2" contributes a digital sum of 3, hence the total is divisible by 3. Is there a semiprime in the sequence after 21? - Jonathan Vos Post, Jul 18 2012
The semiprime subsequence contains 21, 11222121, 12122211, 21221121, 22211121, 22212111, and continues with 14 10-digit entries etc. - R. J. Mathar, Jul 19 2012
|
|
REFERENCES
|
J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 2.
|
|
LINKS
|
|
|
MAPLE
|
sort([seq(seq((10^(2*d)-1)/9+add(10^i, i=s), s=combinat:-choose([$0..(2*d-1)], d)), d=1..4)]); # Robert Israel, Jan 02 2018
|
|
MATHEMATICA
|
Sort[FromDigits/@Flatten[Table[Permutations[PadRight[{}, 2n, {1, 2}]], {n, 3}], 1]] (* Harvey P. Dale, Aug 30 2016 *)
|
|
PROG
|
(Python)
from itertools import count, islice
from sympy.utilities.iterables import multiset_permutations as mp
def agen():
for d in count(2, 2):
for s in mp("1"*(d//2) + "2"*(d//2), d):
yield int("".join(s))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|