A228288 Smallest k such that z = n in the minimal value of x + y*z, given x*y + z = k (for positive integers x, y, z).

2, 8, 48, 160, 720, 790, 1690, 4572, 13815, 22031, 22032, 79965, 209013, 546035, 546036, 546037, 2932793, 2037794, 2932795, 12433772, 17529248, 9945922, 72105623, 72105624, 72105625, 195099674, 205216242, 222426196, 222426197, 984126926

Offset

1,1

Comments

The first decrease in the sequence is at a(17) > a(18). [Andy Niedermaier, Sep 01 2013]

No value of z larger than 25 appears in the first 10^8 terms of A228287.

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = min {k: A228287(k)=n}. Smallest greedy inverse of A228287. - R. J. Mathar, Sep 02 2013

Example

For n = 3, a(n) = 48. This is because for 2 <= n < 48, z = 1 or z = 2 in the smallest value of x + yz (given xy + z = n). But for xy + z = 48, the minimal x + yz is given for (x, y, z) = (15, 3, 3).
In cases where multiple triples (x, y, z) achieve the smallest value for x + yz, we consider the triple with the smaller value of z. (See A228287.) Thus, even though for n = 215, (53, 4, 3) and (35, 6, 5) give the minimum value for x + yz, a(5) cannot equal 215. (720 is the smallest n for which we MUST have z = 5 in order to achieve the minimum x + yz.)

Crossrefs

Cf. A228286, A228287.

Sequence in context: A003032 A193944 A058928 * A356346 A292277 A173841

Adjacent sequences: A228285 A228286 A228287 * A228289 A228290 A228291

Keyword

nonn

Author

Andy Niedermaier, Aug 19 2013

Extensions

Added terms a(17) through a(25). - Andy Niedermaier, Sep 02 2013

Added terms a(26) through a(30). - Andy Niedermaier, Sep 11 2013

Status

approved