|
| |
|
|
A171225
|
|
Nonnegative numbers which cannot be represented by inserting plus or minus signs between the digits of 123456789.
|
|
0
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
|
|
|
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
|
|
|
|
KEYWORD
|
nonn,easy,base
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
Definition rephrased, terms beyond 300 added by R. J. Mathar, Dec 07 2009
|
|
|
STATUS
|
approved
|
| |
|
|
