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A296713
Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.
3
12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 56, 57, 58, 59, 67, 68, 69, 78, 79, 89, 112, 113, 114, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 133, 134, 135, 136, 137, 138, 139
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 A296712-A296714 partition the natural numbers. See the guide at A296712.
LINKS
EXAMPLE
The base-10 digits of 139 are 1,3,9; here #(rises) = 2 and #(falls) = 0, so 139 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 *)
Select[Range[150], Total[Sign[Differences[IntegerDigits[#]]]]>0&] (* Harvey P. Dale, May 21 2021 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 08 2018
STATUS
approved