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A117204
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Squarefree positive integers k such that 2*k+1 is also squarefree.
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6
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1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 17, 19, 21, 23, 26, 29, 30, 33, 34, 35, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 59, 61, 65, 66, 69, 70, 71, 74, 77, 78, 79, 82, 83, 86, 89, 91, 93, 95, 97, 101, 102, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118, 119
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OFFSET
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1,2
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COMMENTS
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The asymptotic density of this sequence is (3/2)*A065474 = 0.4839511484... (Erdős and Ivić, 1987). - Amiram Eldar, Mar 02 2021
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LINKS
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FORMULA
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EXAMPLE
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10 and 2*10 +1 = 21 are both squarefree, so 10 is in the sequence.
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MATHEMATICA
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sfQ[n_]:=SquareFreeQ[n]&&SquareFreeQ[2n+1]; Select [Range[200], sfQ] (* Harvey P. Dale, Mar 12 2011 *)
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CROSSREFS
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KEYWORD
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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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