|
|
A348167
|
|
Numbers whose binary representation contains a maximal set of nonconsecutive 1's.
|
|
1
|
|
|
1, 2, 5, 9, 10, 18, 21, 37, 41, 42, 73, 74, 82, 85, 146, 149, 165, 169, 170, 293, 297, 298, 329, 330, 338, 341, 585, 586, 594, 597, 658, 661, 677, 681, 682, 1170, 1173, 1189, 1193, 1194, 1317, 1321, 1322, 1353, 1354, 1362, 1365, 2341, 2345, 2346, 2377, 2378
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
These are the numbers that do not contain 11 and 000 in their binary representations (cf. A086638), and in addition do not have 00 as their two lowest-order bits.
|
|
LINKS
|
|
|
EXAMPLE
|
5 is in this sequence, because its binary representation 101 cannot have any more ones added (below its highest nonzero bit) while preserving the property of having no two consecutive 1's.
4 is not in the sequence, because its binary representation 100 can be augmented to 101, producing another number in the sequence.
|
|
PROG
|
(Python)
x = -1
while True:
x = x + 1
if x & (x>>1): continue
if (x & 3) == 0: continue
negx = ~x
gaps = negx & (negx >> 1) & (negx >> 2)
if (gaps-1) & x != x: continue
yield x
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|