%I
%S 160,178,196,211,219,221,223,227,229,233,235,237,239,241,247,250,253,
%T 259,274,277,284,286,287,292,295,300,302,304,309,310,312,313,319,325,
%U 331,337,349,363,367,368,372,377,381,382,385,388,390,391,392,395,397,399,400,401
%N Nonnegative numbers which cannot be represented by inserting plus or minus signs between the digits of 123456789.
%C a(1)=160 is the smallest number which can't be described by such expressions.
%C 159 has 6 ways to reach it: 159 = 123456+78+9 = 123+4+56789 = 1+234+5+6789 = 1+23+456+7+89 = 123456+7+89 = 12+34+5+67+89.
%C There are 3^8=6561 ways to form expressions of that kind, including duplicates and negative numbers.  _R. J. Mathar_, Dec 07 2009
%o (Excel) VBA Program:
%o Sub Test() Dim Solutions(1 To 1000), result As Single Dim temp As Long, x(1 To 17) As String, op Dim i As Long, j As Long, out As String, num As Long op = Array("+", "", "") For i = 1 To 9 x(2 * i  1) = i Next For i = 0 To 3 ^ 8  1 temp = i For j = 1 To 8 x(2 * j) = op(temp Mod 3) temp = temp \ 3 Next out = Join(x, "") result = Evaluate(out) If result > 0 Then If result < 1001 Then Solutions(result) = Solutions(result) + 1 End If End If Next For i = 1 To 1000 If Solutions(i) = 0 Then Debug.Print i; Next End Sub
%Y Cf. A066956.
%K nonn,easy,base
%O 1,1
%A _Zhining Yang_, Dec 05 2009
%E Definition rephrased, terms beyond 300 added by _R. J. Mathar_, Dec 07 2009
