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A296706
Numbers whose base-8 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.
4
1, 2, 3, 4, 5, 6, 7, 9, 18, 27, 36, 45, 54, 63, 65, 66, 67, 68, 69, 70, 71, 73, 80, 81, 88, 89, 90, 96, 97, 98, 99, 104, 105, 106, 107, 108, 112, 113, 114, 115, 116, 117, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 135, 138, 139, 140
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 A296706-A296707 partition the natural numbers. See the guide at A296712.
LINKS
EXAMPLE
The base-8 digits of 140 are 2,1,4; here #(rises) = 1 and #(falls) = 1, so 140 is in the sequence.
MATHEMATICA
z = 200; b = 8; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296706 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296707 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296708 *)
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Jan 08 2018
STATUS
approved