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A163492
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Numbers such that the two adjacent integers are a perfect square and a prime.
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7
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1, 2, 3, 8, 10, 24, 48, 80, 82, 168, 224, 226, 360, 440, 442, 728, 840, 1088, 1090, 1224, 1368, 1522, 1848, 2026, 2208, 2400, 3024, 3250, 3720, 3968, 4760, 5040, 5624, 5928, 6562, 7920, 8648, 9802, 10608, 11026, 11448, 12322, 13688, 13690, 14160, 14640
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OFFSET
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1,2
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COMMENTS
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Also known as the Beprisque numbers.
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LINKS
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EXAMPLE
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a(1) = 2 since 2 lies between 1(square) and 3(prime).
a(2) = 3 since 3 lies between 2(prime) and 4(square).
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MATHEMATICA
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nn = 100; Sort[Select[Range[0, nn], PrimeQ[#^2 + 2] &]^2 + 1, Select[Range[nn], PrimeQ[#^2 - 2] &]^2 - 1] (* T. D. Noe, Aug 29 2012 *)
Select[Range[15000], AnyTrue[#+{1, -1}, PrimeQ]&&AnyTrue[{Sqrt[#-1], Sqrt[ #+1]}, IntegerQ]&] (* Harvey P. Dale, Feb 06 2023 *)
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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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