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 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

%I

%S 2,7,11,20,25,29,52,65,70,101,110,133,200,205,205,250,254,290,425,502,

%T 520,641,650,700,785,925,1001,1010,1100,1258,1330,2000,2005,2050,2050,

%U 2225,2500,2504,2540,2900,3157,3445,4025,4250,5002,5020

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

%C 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".

%C 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

%C The left-hand 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

%e 1/4 + 1/25 = 0.29 --> 29 is a "sliding number"

%e 1/8 + 1/125 = 0.133 --> 133 is a "sliding number"

%e 1/2 + 1/5 = 0.7 --> 7 is a "sliding number"

%Y Cf. A103183, A103184.

%K nonn

%O 1,1

%A _Eric Angelini_, Mar 09 2005

%E More terms from _Kerry Mitchell_, Mar 09 2005

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Last modified April 9 22:27 EDT 2020. Contains 333382 sequences. (Running on oeis4.)