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A111186
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Difference between the closest squares surrounding squarefree composite numbers.
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0
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5, 5, 7, 7, 7, 7, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19
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OFFSET
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6,1
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LINKS
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FORMULA
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Let n be a squarefree composite number and r = floor(sqrt(n)). Then the closest surrounding squares of n are r^2 and (r+1)^2. So d = (r+1)^2 - r^2 = 2r+1.
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EXAMPLE
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6 is the first positive squarefree composite number. 2^2 and 3^2 are the closest squares surrounding 6. So the difference, 9-4 = 5, is the first entry in the table.
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PROG
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(PARI) surrsq(n) = { local(x, y, j, r, d); for(x=1, n, if(!issquare(x)&!isprime(x), r=floor(sqrt(x)); d=r+r+1; print1(d", ") \ print1(r^2", "(r+1)^2", ") ) ) }
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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