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A296755
Numbers whose base-14 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.
5
14, 28, 29, 42, 43, 44, 56, 57, 58, 59, 70, 71, 72, 73, 74, 84, 85, 86, 87, 88, 89, 98, 99, 100, 101, 102, 103, 104, 112, 113, 114, 115, 116, 117, 118, 119, 126, 127, 128, 129, 130, 131, 132, 133, 134, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 154
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 A296753-A296755 partition the natural numbers. See the guide at A296712.
LINKS
EXAMPLE
The base-14 digits of 10^9 are 9, 6, 11, 4, 11, 6, 11, 6; here #(rises) = 3 and #(falls) = 4, so 10^9 is in the sequence.
MATHEMATICA
z = 200; b = 14; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296753 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296754 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296755 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 08 2018
STATUS
approved