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A039957 Squarefree numbers congruent to 3 mod 4.

%I A039957 #51 Feb 21 2022 01:06:17
%S A039957 3,7,11,15,19,23,31,35,39,43,47,51,55,59,67,71,79,83,87,91,95,103,107,
%T A039957 111,115,119,123,127,131,139,143,151,155,159,163,167,179,183,187,191,
%U A039957 195,199,203,211,215,219,223,227,231,235,239,247,251,255
%N A039957 Squarefree numbers congruent to 3 mod 4.
%C A039957 Negatives of odd fundamental discriminants D := b^2-4*a*c<0 of definite integer binary quadratic forms F=a*x^2+b*x*y+c*y^2. See Buell reference pp. 224-230. See 4*A089269 = A191483 for the even case and A003657 for combined even and odd numbers. - _Wolfdieter Lang_, Nov 07 2003
%C A039957 The asymptotic density of this sequence is 2/Pi^2 = 0.202642... (A185197). - _Amiram Eldar_, Feb 10 2021
%D A039957 Richard A. Mollin, Quadratics, CRC Press, 1996, Tables B1-B3.
%D A039957 Duncan A. Buell, Binary Quadratic Forms, Springer-Verlag, NY, 1989.
%H A039957 Reinhard Zumkeller, <a href="/A039957/b039957.txt">Table of n, a(n) for n = 1..10000</a>
%H A039957 A. M. Legendre, <a href="https://books.google.fr/books?id=EBtPMqDlPxcC&amp;pg=PA488#v=twopage&amp;q&amp;f=false">Diviseurs de la forme t^2+au^2 a étant un nombre de la forme 4n-1</a>, Essai sur la Théorie des Nombres An VI, Table V.
%t A039957 fQ[n_] := SquareFreeQ[n] && Mod[n, 4] == 3; Select[ Range@ 258, fQ] (* _Robert G. Wilson v_, Mar 02 2011 *)
%t A039957 Select[Range[3,300,4],SquareFreeQ] (* _Harvey P. Dale_, Mar 08 2015 *)
%o A039957 (Magma) [4*n+3: n in [0..63] | IsSquarefree(4*n+3)];  // _Bruno Berselli_, Mar 04 2011
%o A039957 (Haskell)
%o A039957 a039957 n = a039957_list !! (n-1)
%o A039957 a039957_list = filter ((== 3) . (`mod` 4)) a005117_list
%o A039957 -- _Reinhard Zumkeller_, Aug 15 2011
%o A039957 (PARI) is(n)=n%4==3 && issquarefree(n) \\ _Charles R Greathouse IV_, Feb 07 2017
%Y A039957 Cf. A039955, A039956, A185197, A191483.
%K A039957 nonn,easy,nice
%O A039957 1,1
%A A039957 _R. K. Guy_
%E A039957 Offset corrected