A139491 Numbers arising in A139490.

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

Offset: 1

Author

Artur Jasinski, Apr 24 2008, Apr 26 2008

Keywords

• nonn

Comments

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.

This sequence is a subsequence of A024352.

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

Links

• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A000926, A024352.

Programs

Mathematica

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]

Extensions

Extended by T. D. Noe, Apr 27 2009