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A222030
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Primes and quarter-squares.
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2
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0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 16, 17, 19, 20, 23, 25, 29, 30, 31, 36, 37, 41, 42, 43, 47, 49, 53, 56, 59, 61, 64, 67, 71, 72, 73, 79, 81, 83, 89, 90, 97, 100, 101, 103, 107, 109, 110, 113, 121, 127, 131, 132, 137, 139, 144, 149, 151, 156, 157, 163, 167, 169
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OFFSET
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0,3
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COMMENTS
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It appears that there is always a prime between two consecutive quarter squares, if n >= 2. Therefore in a square spiral, or zig-zag, whose vertices are the quarter-squares, it appears that there is always a prime between two consecutive vertices, if n >= 2.
Apparently the above comment is equivalent to the Oppermann's conjecture. - Omar E. Pol, Oct 26 2013
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LINKS
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FORMULA
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MATHEMATICA
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mx = 13; Union[Prime[Range[PrimePi[mx^2]]], Floor[Range[2*mx]^2/4]] (* Alonso del Arte, Mar 03 2013 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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