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A343760 Numbers whose digits can be the lengths of the sides of a polygon.

%I A343760 #31 May 16 2021 09:28:40
%S A343760 111,122,133,144,155,166,177,188,199,212,221,222,223,232,233,234,243,
%T A343760 244,245,254,255,256,265,266,267,276,277,278,287,288,289,298,299,313,
%U A343760 322,323,324,331,332,333,334,335,342,343,344
%N A343760 Numbers whose digits can be the lengths of the sides of a polygon.
%C A343760 The length of each side must be greater than 0 and less than the sum of the other sides.
%C A343760 Subset of the 0-free numbers, A052382, and eventually contains all the 0-free numbers > 9111111111.
%H A343760 Maths StackExchange, <a href="https://math.stackexchange.com/questions/3183931/the-no-of-possible-3-digit-number-abc-if-a-b-c-are-the-sides-of-a-isoscel">The no. of possible 3 digit number abc if a,b,c are the sides of a isosceles triangle</a>.
%H A343760 Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%e A343760 110 is not a term since the 3rd side has a length of 0.
%e A343760 111 is a term since a polygon (in this case a triangle) can have sides of length 1,1,1.
%e A343760 112 is not a term since the length of the 3rd side is not less than the sum of the other two sides.
%t A343760 Select[Range[111, 344], AllTrue[TakeDrop[#, 1] & /@ Permutations@ IntegerDigits[#], First[#1] < Total[#2] & @@ # &] &] (* _Michael De Vlieger_, May 01 2021 *)
%o A343760 (Java)
%o A343760 public class A343760 {
%o A343760    public static void main(String[] args) {
%o A343760       for (long n = 1; n < 1000; n++) {
%o A343760          if (is(n)) {
%o A343760             System.out.print(n + ", ");
%o A343760          }
%o A343760       }
%o A343760    }
%o A343760    public static boolean is(long n) {
%o A343760       String s = String.valueOf(n);
%o A343760       if (n < 0 || s.contains("0")) {
%o A343760          return false;
%o A343760       }
%o A343760       int perimeter = 0;
%o A343760       char[] sides = s.toCharArray();
%o A343760       for (int i = 0; i < sides.length; i++) {
%o A343760          sides[i] -= '0';
%o A343760          perimeter += sides[i];
%o A343760       }
%o A343760       for (int side : sides) {
%o A343760          if (perimeter <= 2 * side) {
%o A343760             return false;
%o A343760          }
%o A343760       }
%o A343760       return true;
%o A343760    }
%o A343760 }
%Y A343760 Cf. A052382.
%K A343760 base,nonn
%O A343760 1,1
%A A343760 _John R Phelan_, Apr 27 2021