A228287 Smallest value of z in the minimal value of x + y*z, given x + y*z = n (where x, y, z are positive integers).

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 2, 3, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1

Offset

2,7

Comments

If there are multiple triples (x, y, z) for which xy + z = n and x + yz is minimized, consider the triple with smallest z. I.e., this sequence illustrates the smallest z needed to minimize x + yz.

For n = 215 the triples (53, 4, 3) and (35, 6, 5) both give the minimal value of x + yz = 65. Thus a(215) = 3.

Links

Table of n, a(n) for n=2..88.

Maple

A228287 := proc(n)
    local a, x, y, z, zfin ;
    a := n+n^2 ;
    zfin := n ;
    for z from 1 to n-1 do
        for x in numtheory[divisors](n-z) do
            y := (n-z)/x ;
            if x+y*z < a then
                a := x+y*z ;
                zfin := z ;
            end if;
        end do:
    end do:
    return zfin;
end proc: # R. J. Mathar, Sep 02 2013

Mathematica

A228287[n_] := Module[{a, x, y, z, zfin}, a = n + n^2; zfin = n; Do[Do[y = (n-z)/x; If[x + y*z < a, a = x + y*z; zfin = z], {x, Divisors[n-z]}], {z, 1, n-1}]; zfin];
Table[A228287[n], {n, 2, 100}] (* Jean-François Alcover, Aug 08 2023, after R. J. Mathar *)

Crossrefs

Cf. A228286.

Sequence in context: A307614 A363057 A242481 * A213636 A192393 A184303

Adjacent sequences: A228284 A228285 A228286 * A228288 A228289 A228290

Keyword

nonn

Author

Andy Niedermaier, Aug 19 2013

Status

approved