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A162719
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A positive integer n is included if n in binary contains as many 0's as the number of 1's in the binary representation of n+1, and if n in binary contains as many 1's as the number of 0's in the binary representation of n+1.
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0
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4, 9, 18, 19, 20, 24, 37, 39, 41, 49, 70, 74, 75, 76, 79, 82, 83, 84, 88, 98, 99, 100, 104, 112, 141, 149, 151, 153, 159, 165, 167, 169, 177, 197, 199, 201, 209, 225, 270, 278, 282, 283, 284, 294, 298, 299, 300, 303, 306, 307, 308, 312, 319, 326, 330, 331, 332
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OFFSET
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1,1
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LINKS
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EXAMPLE
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39 in binary is 100111, which has two 0's and four 1's. 39+1 = 40 is 101000 in binary, which contains two 1's and four 0's. Since the number of 0's in binary 39 equals the number of 1's in binary 40, and because the number of 1's in binary 39 equals the number of 0's in binary 40, then 39 is in the sequence.
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MAPLE
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read("transforms") ; A070939 := proc(n) max(1, ilog2(n)+1) ; end: A023416 := proc(n) A070939(n)-wt(n) ; end: isA162719 := proc(n) RETURN( A023416(n) = wt(n+1) and wt(n) = A023416(n+1)) ; end: for n from 1 to 999 do if isA162719(n) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Aug 01 2009
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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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