A004750 Numbers whose binary expansion contains the substring '011'.

11, 19, 22, 23, 27, 35, 38, 39, 43, 44, 45, 46, 47, 51, 54, 55, 59, 67, 70, 71, 75, 76, 77, 78, 79, 83, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 99, 102, 103, 107, 108, 109, 110, 111, 115, 118, 119, 123, 131, 134, 135, 139, 140, 141, 142, 143, 147, 150

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base

Examples

			19 is in the sequence because 19 = 10011_2 and '10011' has '011' as one of its substrings. - _Indranil Ghosh_, Feb 11 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..32769 (terms 1..1001 from Harvey P. Dale)
• Index entries for 2-automatic sequences.

Crossrefs

Cf. A004749, A004751, A004752, A004753.

Programs

Mathematica

Select[Range[200],MemberQ[Partition[IntegerDigits[#,2],3,1],{0,1,1}]&] (* Harvey P. Dale, Apr 14 2014 *)
Select[Range[200],SequenceCount[IntegerDigits[#,2],{0,1,1}]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 01 2021 *)

PARI

is(n)=while(n>10, if(bitand(n, 7)==3, return(1)); n>>=1); 0 \\ Charles R Greathouse IV, Feb 11 2017

Python

i=j=0
while j<=100:
    if "011" in bin(i)[2:]:
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Feb 11 2017

Formula

a(n) ~ n. - Charles R Greathouse IV, Oct 23 2015

Extensions

Offset corrected by Charles R Greathouse IV, Feb 11 2017