A004748 Binary expansion contains 101.

5, 10, 11, 13, 20, 21, 22, 23, 26, 27, 29, 37, 40, 41, 42, 43, 44, 45, 46, 47, 52, 53, 54, 55, 58, 59, 61, 69, 74, 75, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 101, 104, 105, 106, 107, 108, 109, 110, 111, 116, 117, 118, 119, 122

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Examples

			20 is in the sequence because 20 = 10100_2. '10100' has '101' 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. A004749, A004750, A004751, A004752, A004753.

Programs

Mathematica

Select[Range[200], MemberQ[Partition[IntegerDigits[#, 2], 3, 1], {1, 0, 1}] &] (* Vincenzo Librandi, Feb 17 2018 *)
Select[Range[200],SequenceCount[IntegerDigits[#,2],{1,0,1}]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 01 2020 *)

PARI

is(n)=while(n>4,if(bitand(n,7)==5, return(1)); n>>=1); 0 \\ Charles R Greathouse IV, Feb 11 2017

Python

i=j=0
while j<=100:
    if "101" 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