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Numbers such that the two adjacent integers are a perfect square and a prime.
7

%I #11 Feb 06 2023 19:24:25

%S 1,2,3,8,10,24,48,80,82,168,224,226,360,440,442,728,840,1088,1090,

%T 1224,1368,1522,1848,2026,2208,2400,3024,3250,3720,3968,4760,5040,

%U 5624,5928,6562,7920,8648,9802,10608,11026,11448,12322,13688,13690,14160,14640

%N Numbers such that the two adjacent integers are a perfect square and a prime.

%C Also known as the Beprisque numbers.

%H T. D. Noe, <a href="/A163492/b163492.txt">Table of n, a(n) for n = 1..1000</a>

%H Planet Math, <a href="http://planetmath.org/BeprisqueNumber.html">Beprisque numbers</a>

%e a(1) = 2 since 2 lies between 1(square) and 3(prime).

%e a(2) = 3 since 3 lies between 2(prime) and 4(square).

%t 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 *)

%t Select[Range[15000],AnyTrue[#+{1,-1},PrimeQ]&&AnyTrue[{Sqrt[#-1],Sqrt[ #+1]},IntegerQ]&] (* _Harvey P. Dale_, Feb 06 2023 *)

%Y Cf. A051700, A066635.

%K nonn

%O 1,2

%A _Gaurav Kumar_, Jul 29 2009

%E Definition clarified by _R. J. Mathar_, Aug 08 2009

%E Number 1 added by _WG Zeist_, Aug 28 2012