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Search: id:A111213
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| A111213 |
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Difference between the closest squares surrounding prime p is prime. |
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+0
1
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| 3, 3, 5, 5, 7, 7, 11, 11, 13, 13, 13, 13, 17, 17, 17, 17, 19, 19, 19, 23, 23, 23, 23, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 37, 37, 41, 41, 41, 41, 41, 41, 41, 43, 43, 43, 43, 43, 43, 43, 47, 47, 47, 47, 47, 47
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Conjecture: The number of terms in this sequence is infinite.
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FORMULA
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Let p be a prime number and r = floor(sqrt(p)). Then the closest surrounding squares of p are r^2 and (r+1)^2. So d = (r+1)^2 - r^2 = 2r+1. If if d is prime then list d.
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EXAMPLE
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29 is a prime number. 5^2 and 6^2 are the closest squares surrounding 29. Now
the difference, 36-25 = 11 is prime so 11 is in the table.
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PROGRAM
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(PARI) surrsqpr(n) = { local(x, y, j, r, d); forprime(x=2, n, r=floor(sqrt(x)); d=r+r+1; if(isprime(d), print1(d", ") ) ) }
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CROSSREFS
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Sequence in context: A109613 A073737 A133908 this_sequence A095878 A077381 A157966
Adjacent sequences: A111210 A111211 A111212 this_sequence A111214 A111215 A111216
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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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