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Squares of the form p*q - p - q + 2, where p and q are primes.
1

%I #8 Apr 20 2024 10:22:33

%S 9,25,49,81,121,169,225,289,361,529,625,841,961,1225,1369,1521,1681,

%T 1849,2025,2209,2401,2601,2809,3025,3481,3721,4225,4489,4761,5041,

%U 5329,5929,6241,6889,7225,7921,8281,9025,9409,10201,10609,11449,11881,12769

%N Squares of the form p*q - p - q + 2, where p and q are primes.

%C Includes A108570 squares of lesser twin primes and A110284 squares of form 4p-3 where p is prime (q=5).

%t Lim=13000;f[{p_,q_}]:=p*q-p-q+2;Union[Select[f/@Subsets[Prime[Range[PrimePi[Lim]]], {2}],#<Lim&&IntegerQ[Sqrt[#]]&]] (* _James C. McMahon_, Apr 20 2024 *)

%Y Cf. A108570, A110284, A110484.

%K nonn

%O 1,1

%A _Giovanni Teofilatto_, Sep 11 2005

%E Corrected and extended by _Ray Chandler_, Sep 13 2005