A173024 -id:A173024 - cp's OEIS frontend

A144795 A positive integer n is included if every 1 in binary n is next to at least one other 1.

3, 6, 7, 12, 14, 15, 24, 27, 28, 30, 31, 48, 51, 54, 55, 56, 59, 60, 62, 63, 96, 99, 102, 103, 108, 110, 111, 112, 115, 118, 119, 120, 123, 124, 126, 127, 192, 195, 198, 199, 204, 206, 207, 216, 219, 220, 222, 223, 224, 227, 230, 231, 236, 238, 239, 240, 243, 246

Offset: 1

Leroy Quet, Sep 21 2008

n is included if A144790(n) >= 2.

A173024 is a subsequence. - Reinhard Zumkeller, Feb 07 2010

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A144790, A144794.
Cf. A004760, A173022, A005251, A173025. - Reinhard Zumkeller, Feb 07 2010
Complement of A377169.

isA144795 := proc(n) local bind,i ; bind := convert(n,base,2) ; for i from 1 to nops(bind) do if i = 1 then if op(i,bind) = 1 and op(i+1,bind) = 0 then RETURN(false) : fi; elif i = nops(bind) then if op(i,bind) = 1 and op(i-1,bind) = 0 then RETURN(false) : fi; else if op(i,bind) = 1 and op(i-1,bind) = 0 and op(i+1,bind) = 0 then RETURN(false) : fi; fi; od: RETURN(true) ; end: for n from 3 to 400 do if isA144795(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Sep 29 2008

Select[Range@ 250, AllTrue[Map[Length, Select[Split@ IntegerDigits[#, 2], First@ # == 1 &]], # > 1 &] &] (* Michael De Vlieger, Aug 20 2017 *)

Extended by R. J. Mathar, Sep 29 2008

A173021 Number of numbers <= n whose binary representation is without isolated ones or isolated double ones.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11

Offset: 0

Reinhard Zumkeller, Feb 07 2010

			a(30) = #{0, 7, 14, 15, 28, 30} = #{0, 111, 1110, 1111, 11100, 11110} = 6.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A005252, A007088, A173022, A173023, A173024.

ioQ[n_]:=Module[{idn2=Split[IntegerDigits[n,2]]},FreeQ[idn2,{1}]&&FreeQ[ idn2,{1,1}]]; Accumulate[Table[If[ioQ[n],1,0],{n,0,90}]] (* Harvey P. Dale, May 15 2016 *)

a(A173024(n+1)) = a(A173024(n)) + 1.
a(2^n - 1) = A005252(n+1).
a(n) <= A173022(n) <= A173023(n).

A173025 Numbers whose binary representation contains no isolated digits "11".

Original entry on oeis.org

0, 1, 2, 4, 5, 7, 8, 9, 10, 14, 15, 16, 17, 18, 20, 21, 23, 28, 29, 30, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 46, 47, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 68, 69, 71, 72, 73, 74, 78, 79, 80, 81, 82, 84, 85, 87, 92, 93, 94, 95, 112, 113, 114, 116, 117, 119, 120, 121, 122

Offset: 1

Reinhard Zumkeller, Feb 07 2010

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A007088, A144795, A173021.

A173024 is a subsequence.

Select[Range[0, 150], FreeQ[Split[IntegerDigits[#, 2]], {1, 1}] &] (* Paolo Xausa, Oct 15 2024 *)

A173021(a(n+1)) = A173021(a(n)) + 1.

cp's OEIS Frontend

A144795 A positive integer n is included if every 1 in binary n is next to at least one other 1.

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A173021 Number of numbers <= n whose binary representation is without isolated ones or isolated double ones.

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A173025 Numbers whose binary representation contains no isolated digits "11".

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