|
|
A296712
|
|
Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.
|
|
116
|
|
|
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 120, 121, 130, 131, 132, 140, 141, 142, 143, 150, 151, 152, 153, 154, 160, 161, 162, 163, 164, 165, 170, 171, 172, 173, 174, 175, 176, 180, 181
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296712-A296714 partition the natural numbers.
****
Guide to related sequences:
Base #(rises) = #(falls) #(rises) > #(falls) #(rises) < #(falls)
|
|
LINKS
|
|
|
EXAMPLE
|
The base-10 digits of 181 are 1,8,1; here #(rises) = 1 and #(falls) = 1, so 181 is in the sequence.
|
|
MATHEMATICA
|
z = 200; b = 10; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296712 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296713 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296714 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|