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Numbers arising in A139490.
24

%I #22 May 09 2021 07:51:43

%S 3,8,9,12,15,16,21,24,40,45,48,60,72,120,168,240,840,1848

%N Numbers arising in A139490.

%C _M. F. Hasler_, Apr 24 2008, observed that the numbers in this sequence are differences of two squares. For example: 3=2^2-1^2, 8=3^2-1^2, 9=5^2-4^2, 15=4^2-1^2, 16=5^2-3^2, 21=5^2-2^2, 24=5^2-1^2, 40=7^2-3^2, 45=7^2-2^2, 48=7^2-1^2, 60=8^2-2^2.

%C This sequence is a subsequence of A024352.

%C These numbers appear to be a subset of the idoneal numbers A000926. If so, then the sequence is probably complete. - _T. D. Noe_, Apr 27 2009

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

%t f = 200; g = 300; h = 30; j = 100; b = {}; Do[a = {}; Do[Do[If[PrimeQ[x^2 + n y^2], AppendTo[a, x^2 + n y^2]], {x, 0, g}], {y, 1, g}]; AppendTo[b, Take[Union[a], h]], {n, 1, f}]; Print[b]; c = {}; Do[a = {}; Do[Do[If[PrimeQ[n^2 + w*n*m + m^2], AppendTo[a, n^2 + w*n*m + m^2]], {n, m, g}], {m, 1, g}]; AppendTo[c, Take[Union[a], h]], {w, 1, j}]; Print[c]; bb = {}; cc = {}; Do[Do[If[b[[p]] == c[[q]], AppendTo[bb, p]; AppendTo[cc, q]], {p, 1, f}], {q, 1, j}]; Union[bb]

%Y Cf. A000926, A024352.

%K nonn

%O 1,1

%A _Artur Jasinski_, Apr 24 2008, Apr 26 2008

%E Extended by _T. D. Noe_, Apr 27 2009