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A296707
Numbers whose base-8 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.
4
10, 11, 12, 13, 14, 15, 19, 20, 21, 22, 23, 28, 29, 30, 31, 37, 38, 39, 46, 47, 55, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 91, 92, 93, 94, 95, 100, 101, 102, 103, 109, 110, 111, 118, 119, 127, 147, 148, 149, 150, 151, 155, 156, 157, 158, 159, 164
OFFSET
1,1
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 164 are 2,4,4; here #(rises) = 1 and #(falls) = 0, so 164 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