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A143070
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A positive integer n is included if the number of 0's in the binary representation of n is a power of 2 (including being possibly 1).
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3
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2, 4, 5, 6, 9, 10, 11, 12, 13, 14, 16, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 47, 48, 51, 53, 54, 55, 57, 58, 59, 60, 61, 62, 67, 69, 70, 73, 74, 76, 79, 81, 82, 84, 87, 88, 91, 93, 94, 95, 97, 98, 100, 103, 104, 107, 109, 110, 111, 112, 115
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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34 in binary is 100010. This has 4 zeros. And since 4 is a power of 2, 34 is included in the sequence.
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MAPLE
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a:=proc(n) local nn, n0: nn:=convert(n, base, 2): n0:=nops(nn)-add(nn[j], j=1.. nops(nn)): if 0 < n0 and type(log[2](n0), integer)=true then n else end if end proc: seq(a(n), n=1..100); #Emeric Deutsch,Aug 11 2008
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MATHEMATICA
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Select[Range@ 120, IntegerQ@ Log2@ DigitCount[#, 2, 0] &] (*Michael De Vlieger,Oct 25 2017 *)
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PROG
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(Haskell)
a143070 n = a143070_list!! (n-1)
a143070_list = filter ((== 1). a209229. a023416) [1..]
(PARI) ispow2(n) = (n==1) || (n==2) || (ispower(n,, &k) && (k==2));
isok(n) = ispow2(#binary(n) - hammingweight(n)); \\Michel Marcus,Oct 26 2017
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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