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Search: id:A111186
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| A111186 |
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Difference between the closest squares surrounding squarefree composite numbers. |
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+0
1
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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
(list; graph; listen)
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OFFSET
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6,1
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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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PROGRAM
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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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Sequence in context: A139261 A021646 A133888 this_sequence A127798 A053671 A028278
Adjacent sequences: A111183 A111184 A111185 this_sequence A111187 A111188 A111189
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Nov 12 2005
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