

A103182


Sliding numbers: numbers n of the form n = r+s where 1/r + 1/s = (r+s)/10^k for some k >= 1.


2



2, 7, 11, 20, 25, 29, 52, 65, 70, 101, 110, 133, 200, 205, 205, 250, 254, 290, 425, 502, 520, 641, 650, 700, 785, 925, 1001, 1010, 1100, 1258, 1330, 2000, 2005, 2050, 2050, 2225, 2500, 2504, 2540, 2900, 3157, 3445, 4025, 4250, 5002, 5020
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OFFSET

1,1


COMMENTS

Note that 1/20 + 1/50 = 0.70 > 70 is a "sliding number" though 0.70 is usually written 0.7 So any "sliding number" G produces an infinite chain of others : G*10, G*100, G*1000, etc. The first number in such a chain is called "primitive".
Another characterization of the sliding numbers is numbers of the form a + 10^k/a where a  10^k (k >= 0).  David W. Wilson, Mar 09 2005
The lefthand side is (a+b)/ab and we can cancel out (a+b), so we are looking for all (a+b) with a and b positive integers, such that a*b is a (nonnegative integral) power of 10, sorted by (a+b). It follows for example that for a given k, the smallest (a+b) with that k is 2*sqrt(10^k) (equality when k i even, unless we also require a!=b).  Chris Landauer (cal(AT)rushg.aero.org), Mar 10 2005


LINKS

Table of n, a(n) for n=1..46.


EXAMPLE

1/4 + 1/25 = 0.29 > 29 is a "sliding number"
1/8 + 1/125 = 0.133 > 133 is a "sliding number"
1/2 + 1/5 = 0.7 > 7 is a "sliding number"


CROSSREFS

Cf. A103183, A103184.
Sequence in context: A139603 A141183 A308724 * A160698 A294114 A144707
Adjacent sequences: A103179 A103180 A103181 * A103183 A103184 A103185


KEYWORD

nonn


AUTHOR

Eric Angelini, Mar 09 2005


EXTENSIONS

More terms from Kerry Mitchell, Mar 09 2005


STATUS

approved



