A359205 Numbers that have at least two non-overlapping pairs of consecutive ones in their binary representation.

15, 27, 30, 31, 47, 51, 54, 55, 59, 60, 61, 62, 63, 79, 91, 94, 95, 99, 102, 103, 107, 108, 109, 110, 111, 115, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 143, 155, 158, 159

Offset: 1

Author

Elijah Beregovsky, Dec 23 2022

Keywords

• nonn
• base
• easy

Comments

These are the numbers for which the smallest Hamming distance to a fibbinary number is larger than 1.

Examples

			27 is 11011 in binary, thus it is in the sequence.
14 is 1110 in binary. The pairs of consecutive ones overlap, so it is not in the sequence.
		

Links

• Wikipedia, Hamming distance
• Wikipedia, Fibbinary number

Crossrefs

Cf. A003714.

Programs

Mathematica

n=10;
a=Range[2^n];
fib=Select[a, BitAnd[#,2#]==0&];
nonadj=Complement[a,Union@@Outer[BitXor,fib,2^#&/@Range[n]]]