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A101082
Numbers n such that binary representation contains bit strings "10" and "01" (possibly overlapping).
15
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
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
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 one-digit 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 !! (n-1)
a101082_list = filter ((> 0) . a049502) [0..]
-- Reinhard Zumkeller, Jun 17 2015
CROSSREFS
Complement: A023758.
Sequence in context: A325204 A163670 A187713 * A277706 A300669 A166934
KEYWORD
nonn,easy
AUTHOR
Rick L. Shepherd, Nov 29 2004
STATUS
approved