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

Author

David Eppstein, Oct 03 2021

Keywords

• nonn
• base

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.

Examples

			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.
		

Crossrefs

Subsequence of A003714 and A086638.

Programs

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