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A296695
Numbers whose base-4 digits d(m), d(m-1), ... d(0) have #(rises) > #(falls); see Comments.
4
6, 7, 11, 22, 23, 26, 27, 31, 43, 47, 70, 71, 75, 86, 87, 90, 91, 95, 97, 98, 99, 102, 103, 106, 107, 108, 109, 110, 111, 113, 114, 115, 118, 119, 123, 127, 134, 135, 139, 155, 171, 175, 177, 178, 179, 182, 183, 187, 191, 198, 199, 203, 219, 262, 263, 267
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 A296694-A296696 partition the natural numbers. See the guide at A296712.
LINKS
EXAMPLE
The base-4 digits of 267 are 1,0,0,2,3; here #(rises) = 2 and #(falls) = 1, so 267 is in the sequence.
MATHEMATICA
z = 200; b = 4; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296694 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296695 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296696 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Clark Kimberling, Dec 21 2017
STATUS
approved