A086638 -id:A086638 - cp's OEIS frontend

A319423 Indices of records in A175046.

1, 2, 4, 5, 9, 10, 18, 20, 21, 37, 41, 42, 74, 82, 84, 85, 149, 165, 169, 170, 298, 330, 338, 340, 341, 597, 661, 677, 681, 682, 1194, 1322, 1354, 1362, 1364, 1365, 2389, 2645, 2709, 2725, 2729, 2730, 4778, 5290, 5418, 5450, 5458, 5460, 5461, 9557

Offset: 1

N. J. A. Sloane, Sep 23 2018

nonn

a(n) in binary is either an alternating string of 1's and 0's, or exactly one of the 0's is replaced by 00 (see paper in links). - Chai Wah Wu, Oct 04 2018

Chai Wah Wu, Table of n, a(n) for n = 1..10099
Chai Wah Wu, Record values in appending and prepending bitstrings to runs of binary digits, arXiv:1810.02293 [math.NT], 2018

Cf. A086638, A175046, A319422, A319424.

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

Original entry on oeis.org

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

David Eppstein, Oct 03 2021

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.

			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.

Subsequence of A003714 and A086638.

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

cp's OEIS Frontend

A319423 Indices of records in A175046.

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

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