A136318 Integers whose binary representation contains exactly two 1s, the 1s not being adjacent.

5, 9, 10, 17, 18, 20, 33, 34, 36, 40, 65, 66, 68, 72, 80, 129, 130, 132, 136, 144, 160, 257, 258, 260, 264, 272, 288, 320, 513, 514, 516, 520, 528, 544, 576, 640, 1025, 1026, 1028, 1032, 1040, 1056, 1088, 1152, 1280, 2049, 2050, 2052, 2056, 2064, 2080, 2112, 2176

Offset: 1

Author

Gil Broussard, Mar 24 2008

Keywords

• nonn
• easy
• base

Comments

Subsequence of A018900. - Chai Wah Wu, Apr 07 2025

Examples

			a(1) = 5 = 101_2.
a(2) = 9 = 1001_2.
a(3) = 10 = 1010_2.
a(100) = 33024 = 1000000100000000_2.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..99 from Gil Broussard)

Crossrefs

Cf. A018900, A173589.

Programs

Mathematica

Select[Range[2500],DigitCount[#,2,1]==2&&SequenceCount[IntegerDigits[#,2],{1,1}]==0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 25 2017 *)

Python

from math import isqrt, comb
def A136318(n): return (1<<(m:=isqrt(n<<3)+1>>1)+1)+(1<Chai Wah Wu, Apr 07 2025