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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).
1
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.
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
Sequence in context: A193944 A058928 A376029 * A356346 A292277 A173841
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