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A296761
Numbers whose base-16 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.
5
16, 32, 33, 48, 49, 50, 64, 65, 66, 67, 80, 81, 82, 83, 84, 96, 97, 98, 99, 100, 101, 112, 113, 114, 115, 116, 117, 118, 128, 129, 130, 131, 132, 133, 134, 135, 144, 145, 146, 147, 148, 149, 150, 151, 152, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169
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 A296759-A296761 partition the natural numbers. See the guide at A296712.
LINKS
EXAMPLE
The base-16 digits of 32 are 2,0; here #(rises) = 0 and #(falls) = 2, so 32 is in the sequence.
MATHEMATICA
z = 200; b = 16; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296759 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296760 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296761 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 08 2018
STATUS
approved