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

1,1

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

Links

Table of n, a(n) for n=1..54.

Prog

(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

Crossrefs

Cf. A066956.

Sequence in context: A013466 A376899 A060675 * A290463 A367206 A127338

Adjacent sequences: A171222 A171223 A171224 * A171226 A171227 A171228

Keyword

nonn,easy,base

Author

Zhining Yang, Dec 05 2009

Extensions

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

Status

approved