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Numbers whose binary expansion contains the substring '110'.
7

%I #35 Mar 29 2021 15:06:59

%S 6,12,13,14,22,24,25,26,27,28,29,30,38,44,45,46,48,49,50,51,52,53,54,

%T 55,56,57,58,59,60,61,62,70,76,77,78,86,88,89,90,91,92,93,94,96,97,98,

%U 99,100,101,102,103,104,105,106,107,108,109,110,111,112,113

%N Numbers whose binary expansion contains the substring '110'.

%H Indranil Ghosh, <a href="/A004749/b004749.txt">Table of n, a(n) for n = 1..50000</a>

%H <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.

%F a(n) ~ n. - _Charles R Greathouse IV_, Oct 23 2015

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

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

%o (Python)

%o i=j=0

%o while j<=500:

%o if "110" in bin(i)[2:]:

%o print(str(j)+" "+str(i))

%o j+=1

%o i+=1 # _Indranil Ghosh_, Feb 11 2017

%o (PARI) is(n)=while(n>5,if(bitand(n,7)==6, return(1)); n>>=1); 0 \\ _Charles R Greathouse IV_, Feb 11 2017

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

%K nonn,base,easy

%O 1,1

%A _N. J. A. Sloane_

%E Offset corrected by _Charles R Greathouse IV_, Feb 11 2017