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

1,3

Links

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

Formula

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

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 *)

Crossrefs

Cf. A074074.

Sequence in context: A163894 A307095 A032059 * A184186 A004020 A363290

Adjacent sequences: A074072 A074073 A074074 * A074076 A074077 A074078

Keyword

nonn

Author

Lekraj Beedassy, Aug 28 2002

Extensions

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

Status

approved