login
A296693
Numbers whose base-3 digits d(m), d(m-1), ... d(0) have #(rises) < #(falls); see Comments.
4
3, 6, 7, 9, 12, 18, 21, 22, 24, 25, 27, 30, 33, 34, 36, 39, 48, 54, 57, 60, 61, 63, 64, 65, 66, 67, 69, 70, 72, 75, 76, 78, 79, 81, 84, 87, 88, 90, 93, 99, 102, 103, 105, 106, 108, 111, 114, 115, 117, 120, 129, 144, 147, 156, 162, 165, 168, 169, 171, 174
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 A296691-A296693 partition the natural numbers. See the guide at A296712.
LINKS
EXAMPLE
The base-3 digits of 174 are 2,0,1,1,0; here #(rises) = 1 and #(falls) = 2, so 174 is in the sequence.
MATHEMATICA
z = 200; b = 3; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296691 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296692 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296693 *)
rltfQ[n_]:=Module[{d=Differences[IntegerDigits[n, 3]]}, Count[d, _?(#>0&)]<Count[d, _?(#<0&)]]; Select[Range[200], rltfQ] (* Harvey P. Dale, Sep 25 2019 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Clark Kimberling, Dec 19 2017
STATUS
approved