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

Author

Andy Niedermaier, Aug 19 2013

Keywords

• nonn

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.

Examples

			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.

Formula

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