A004749 Numbers whose binary expansion contains the substring '110'.

6, 12, 13, 14, 22, 24, 25, 26, 27, 28, 29, 30, 38, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 70, 76, 77, 78, 86, 88, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Examples

			22 is in the sequence because 22 = 10110_2 and '10110' has '110' as one of its substrings. - _Indranil Ghosh_, Feb 11 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..50000
• Index entries for 2-automatic sequences.

Crossrefs

Cf. A004748, A004750, A004751, A004752, A004753.

Programs

Mathematica

Select[Range[200],SequenceCount[IntegerDigits[#,2],{1,1,0}]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 07 2017 *)

PARI

is(n)=while(n>5,if(bitand(n,7)==6, return(1)); n>>=1); 0 \\ Charles R Greathouse IV, Feb 11 2017

Python

i=j=0
while j<=500:
    if "110" 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