A139491 Numbers arising in A139490.

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

Offset

1,1

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

Table of n, a(n) for n=1..18.

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

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]

Crossrefs

Cf. A000926, A024352.

Sequence in context: A047472 A304204 A028960 * A084387 A080761 A087286

Adjacent sequences: A139488 A139489 A139490 * A139492 A139493 A139494

Keyword

nonn

Author

Artur Jasinski, Apr 24 2008, Apr 26 2008

Extensions

Extended by T. D. Noe, Apr 27 2009

Status

approved