A171225 Nonnegative numbers which cannot be represented by inserting plus or minus signs between the digits of 123456789.

160, 178, 196, 211, 219, 221, 223, 227, 229, 233, 235, 237, 239, 241, 247, 250, 253, 259, 274, 277, 284, 286, 287, 292, 295, 300, 302, 304, 309, 310, 312, 313, 319, 325, 331, 337, 349, 363, 367, 368, 372, 377, 381, 382, 385, 388, 390, 391, 392, 395, 397, 399, 400, 401

Offset: 1

Author

Zhining Yang, Dec 05 2009

Keywords

• nonn
• easy
• base

Comments

a(1)=160 is the smallest number which can't be described by such expressions.

159 has 6 ways to reach it: 159 = 123-45-6+78+9 = 123+4+56-7-8-9 = 1+234+5+6-78-9 = 1+23+45-6+7+89 = 123-4-56+7+89 = 1-2+3-4+5+67+89.

There are 3^8=6561 ways to form expressions of that kind, including duplicates and negative numbers. - R. J. Mathar, Dec 07 2009

Crossrefs

Cf. A066956.

Programs

Excel

VBA Program:
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

Extensions

Definition rephrased, terms beyond 300 added by R. J. Mathar, Dec 07 2009