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A175384
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A positive integer k is included if the largest square dividing k is not equal to the largest square that, when written in binary, occurs as a substring in binary k.
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0
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17, 19, 27, 33, 34, 35, 37, 38, 39, 41, 45, 51, 54, 57, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 89, 90, 97, 99, 101, 102, 103, 105, 108, 113, 114, 115, 117, 125, 126, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 141, 142, 143, 145, 146
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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The largest square dividing 17 is 1. However, 17 in binary is 10001; and the largest square occurring, in its binary representation, within 10001 is 4 (100 in binary). Since 1 does not equal 4, then 17 is in this sequence.
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MAPLE
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A008833 := proc(n) local b; b := floor(sqrt(n)) ; while b >= 1 do if n mod (b^2) = 0 then return b^2 ; end if; b := b-1 ; end do: end proc:
A162400 := proc(n) local b, nbin, a; a := 1 ; nbin := convert(n, base, 2) ; for b from 1 to floor(sqrt(n)) do convert(b^2, base, 2) ; if verify(%, nbin, 'sublist') then a := b^2 ; end if; end do: a ; end proc:
for n from 1 to 300 do if isA162400(n) then printf("%d, ", n) ; end if; end do: (End)
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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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