A074075 - OEIS

%I #12 Mar 27 2024 10:43:40

%S 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,

%T 26,22,19,31,26,33,35,22,29,23,7,31,25,32,37,17,43,28,47,29,49,23,31,

%U 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

%N Values of m corresponding to the minimization problem of A074074.

%H Ray Chandler, <a href="/A074075/b074075.txt">Table of n, a(n) for n = 1..499</a>

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

%t 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]]];

%t a[n_] := a[n] = Sqrt[(2n+1)^2 - A074074[n]]/2;

%t Table[Print[n, " ", a[n]]; a[n], {n, 1, 100}] (* _Jean-François Alcover_, Mar 27 2024 *)

%Y Cf. A074074.

%K nonn

%O 1,3

%A _Lekraj Beedassy_, Aug 28 2002

%E Sequence extended beyond a(7) by _R. J. Mathar_, Sep 21 2009