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A296752
Numbers whose base-13 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.
5
13, 26, 27, 39, 40, 41, 52, 53, 54, 55, 65, 66, 67, 68, 69, 78, 79, 80, 81, 82, 83, 91, 92, 93, 94, 95, 96, 97, 104, 105, 106, 107, 108, 109, 110, 111, 117, 118, 119, 120, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 143, 144
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 A296751-A296753 partition the natural numbers. See the guide at A296712.
LINKS
EXAMPLE
The base-13 digits of 914 are 5,5,4; here #(rises) = 0 and #(falls) = 1, so 914 is in the sequence.
MATHEMATICA
z = 200; b = 13; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296750 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296751 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296752 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 08 2018
STATUS
approved