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Numbers n such that binary representation contains bit strings "10" and "01" (possibly overlapping).
15

%I #29 Feb 12 2017 01:12:44

%S 5,9,10,11,13,17,18,19,20,21,22,23,25,26,27,29,33,34,35,36,37,38,39,

%T 40,41,42,43,44,45,46,47,49,50,51,52,53,54,55,57,58,59,61,65,66,67,68,

%U 69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92

%N Numbers n such that binary representation contains bit strings "10" and "01" (possibly overlapping).

%C Subsequence of A062289; set difference A062289 minus A043569.

%C Complement of A023758. Also numbers not the sum of consecutive powers of 2. - _Omar E. Pol_, Mar 04 2013

%C Equivalently, numbers not the difference of two powers of two. - _Charles R Greathouse IV_, Mar 07 2013

%C The terms >=9 are bases in which a power of 2 exists, which does not contain a digit that is a power of 2. - _Patrick Wienhöft_, Jul 28 2016

%H Reinhard Zumkeller, <a href="/A101082/b101082.txt">Table of n, a(n) for n = 1..10000</a>

%H Patrick Wienhöft, <a href="http://pastebin.com/QqSq72Cy">Python program</a>

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

%F a(n) ~ n. In particular a(n) = n + (log_2 n)^2/2 + O(log n). - _Charles R Greathouse IV_, Mar 07 2013

%F A049502(a(n)) > 0. - _Reinhard Zumkeller_, Jun 17 2015

%e In base 10, 2^16 = 65536 is such a number, as it does not contain any one-digit power of 2, which in base 10 are 1, 2, 4 and 8. - _Patrick Wienhöft_, Jul 28 2016

%t Select[Range@ 120, Function[d, Times @@ Total@ Map[Map[Function[k, Boole@ MatchQ[#, k]], {{1, 0}, {0, 1}}] &, Partition[d, 2, 1]] > 0]@ IntegerDigits[#, 2] &] (* _Michael De Vlieger_, Dec 23 2016 *)

%o (PARI) is(n)=n>>=valuation(n,2);n+1!=1<<valuation(n+1,2) \\ _Charles R Greathouse IV_, Mar 07 2013

%o (Haskell)

%o a101082 n = a101082_list !! (n-1)

%o a101082_list = filter ((> 0) . a049502) [0..]

%o -- _Reinhard Zumkeller_, Jun 17 2015

%Y Complement: A023758.

%Y Cf. A043569, A062289, A049502.

%K nonn,easy

%O 1,1

%A _Rick L. Shepherd_, Nov 29 2004