A084216 a(n) = smallest integer d such that a quadratic representation (2n+1)= x^2+ d*y^2 exists (x,y positive integers).

2, 1, 3, 2, 2, 1, 11, 1, 2, 3, 7, 1, 2, 1, 3, 2, 19, 1, 3, 1, 2, 5, 11, 3, 2, 1, 6, 2, 2, 1, 3, 1, 2, 5, 7, 1, 11, 7, 3, 2, 2, 1, 23, 1, 3, 3, 14, 1, 2, 1, 3, 5, 2, 1, 3, 1, 11, 3, 19, 2, 2, 1, 3, 2, 2, 3, 14, 1, 2, 5, 43, 1, 3, 1, 3, 2, 11, 1, 38, 5, 2, 11, 23, 1, 2, 1, 6, 2, 2, 1, 3, 1, 2, 3, 7, 1, 74, 1

Offset

1,1

Links

Table of n, a(n) for n=1..98.

Example

a(7)=11 because d=11 is the smallest d giving integer solutions x=2,y=1 in
(2*7+1)= x^2+d*y^2 = 2^2 + 11* 1^2 = 15.

Mathematica

<< NumberTheory`NumberTheoryFunctions`; Table[First@Select[Range[100], !MatchQ[t=QuadraticRepresentation[ #, 2n+1], _QuadraticRepresentation]&, 1], {n, 1, 128}]

Crossrefs

Sequence in context: A162348 A262324 A286364 * A347240 A308751 A057514

Adjacent sequences: A084213 A084214 A084215 * A084217 A084218 A084219

Keyword

nonn

Author

Wouter Meeussen, Jun 20 2003

Status

approved