A348167 Numbers whose binary representation contains a maximal set of nonconsecutive 1's.

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

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

Table of n, a(n) for n=1..52.

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)
def A348167():
    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

Subsequence of A003714 and A086638.

Sequence in context: A095347 A249353 A224866 * A159073 A088343 A110781

Adjacent sequences: A348164 A348165 A348166 * A348168 A348169 A348170

Keyword

nonn,base

Author

David Eppstein, Oct 03 2021

Status

approved