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Positive numbers whose decimal expansion contains a 3-digit substring abc such that b > a > c.
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%I #21 Jan 19 2018 02:33:56

%S 120,130,140,150,160,170,180,190,230,231,240,241,250,251,260,261,270,

%T 271,280,281,290,291,340,341,342,350,351,352,360,361,362,370,371,372,

%U 380,381,382,390,391,392,450,451,452,453,460,461,462,463,470,471,472,473

%N Positive numbers whose decimal expansion contains a 3-digit substring abc such that b > a > c.

%C The number of n-digit numbers that start with this substring is 12*10^(n-2), n>=3, hence about 12% of n-digit numbers are of this kind, n>=3. None of the numbers that start with this substring begin with 9.

%e The 3-digit numbers with this substring are 120, 130, ..., 190, ... 890, 891, ..., 897 (there are 120 of these). The next numbers after 879 are 1200, 1201, etc. since they contain the string 120.

%e There are numbers of any length n, n>=3, that contain this substring, such as *231 or 231** where * is free since the substring 231 is already there.

%K nonn,base

%O 1,1

%A _Enrique Navarrete_, Dec 26 2017