A074075 Values of m corresponding to the minimization problem of A074074.

1, 1, 2, 4, 2, 4, 3, 8, 8, 3, 7, 11, 8, 14, 6, 15, 15, 11, 19, 8, 13, 5, 14, 5, 25, 26, 20, 27, 26, 22, 19, 31, 26, 33, 35, 22, 29, 23, 7, 31, 25, 32, 37, 17, 43, 28, 47, 29, 49, 23, 31, 45, 32, 21, 49, 41, 47, 35, 43, 50, 37, 53, 38, 59, 62, 64, 26, 62, 58, 67, 43, 70, 44, 73, 74, 73, 20

Offset: 1

Author

Lekraj Beedassy, Aug 28 2002

Keywords

• nonn

Links

• Ray Chandler, Table of n, a(n) for n = 1..499

Crossrefs

Cf. A074074.

Programs

Mathematica

A074074[n_] := Module[{dd, sols, x, y}, dd = Table[(2n+1)^2 - 4 m^2, {m, 1, n}]; sols = Table[{d, x /. Solve[x > 0 && y > 0 && x^2 - d y^2 == 1, {x, y}, Integers]}, {d, dd}] /. C[1] -> 1 // Select[#, #[[2]] != {}&]&; MinimalBy[sols, #[[2, 1]]&][[1, 1]]];
a[n_] := a[n] = Sqrt[(2n+1)^2 - A074074[n]]/2;
Table[Print[n, " ", a[n]]; a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 27 2024 *)

Formula

a(n) = sqrt( (2n+1)^2-A074074(n))/2 .

Extensions

Sequence extended beyond a(7) by R. J. Mathar, Sep 21 2009