

A101082


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


10



5, 9, 10, 11, 13, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 61, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92
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OFFSET

1,1


COMMENTS

Subsequence of A062289; set difference A062289 minus A043569.
Complement of A023758. Also numbers not the sum of consecutive powers of 2.  Omar E. Pol, Mar 04 2013
Equivalently, numbers not the difference of two powers of two.  Charles R Greathouse IV, Mar 07 2013
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


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Patrick Wienhöft, Python program
Index entries for 2automatic sequences.


FORMULA

a(n) ~ n. In particular a(n) = n + (log_2 n)^2/2 + O(log n).  Charles R Greathouse IV, Mar 07 2013
A049502(a(n)) > 0.  Reinhard Zumkeller, Jun 17 2015


EXAMPLE

In base 10, 2^16 = 65536 is such a number, as it does not contain any onedigit power of 2, which in base 10 are 1, 2, 4 and 8.  Patrick Wienhöft, Jul 28 2016


MATHEMATICA

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 *)


PROG

(PARI) is(n)=n>>=valuation(n, 2); n+1!=1<<valuation(n+1, 2) \\ Charles R Greathouse IV, Mar 07 2013
(Haskell)
a101082 n = a101082_list !! (n1)
a101082_list = filter ((> 0) . a049502) [0..]
 Reinhard Zumkeller, Jun 17 2015


CROSSREFS

Complement: A023758.
Cf. A043569, A062289, A049502.
Sequence in context: A093711 A163670 A187713 * A277706 A300669 A166934
Adjacent sequences: A101079 A101080 A101081 * A101083 A101084 A101085


KEYWORD

nonn,easy


AUTHOR

Rick L. Shepherd, Nov 29 2004


STATUS

approved



