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A296744
Numbers whose base-11 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.
4
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 143, 144, 154, 155, 156, 165, 166, 167, 168, 176, 177, 178, 179, 180, 187, 188, 189, 190, 191, 192, 198, 199, 200, 201, 202, 203
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 A296744-A296746 partition the natural numbers. See the guide at A296712.
LINKS
EXAMPLE
The base-11 digits of 203 are 1,7,5; here #(rises) = 1 and #(falls) = 1, so 203 is in the sequence.
MATHEMATICA
z = 200; b = 11; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296744 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296745 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296746 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 08 2018
STATUS
approved