A296881 Numbers whose base-9 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

99, 100, 108, 109, 110, 117, 118, 119, 120, 126, 127, 128, 129, 130, 135, 136, 137, 138, 139, 140, 144, 145, 146, 147, 148, 149, 150, 153, 154, 155, 156, 157, 158, 159, 160, 189, 190, 191, 198, 199, 200, 201, 207, 208, 209, 210, 211, 216, 217, 218, 219, 220

Offset: 1

Author

Clark Kimberling, Jan 10 2018

Keywords

• nonn
• base
• easy

Comments

A pit is an index i such that d(i-1) > d(i) < d(i+1); a peak is an index i such that d(i-1) < d(i) > d(i+1). The sequences A296879-A296881 partition the natural numbers. See the guides at A296882 and A296712.

Examples

			The base-9 digits of 220 are 2,6,4; here #(pits) = 0 and #(peaks) = 1, so 220 is in the sequence.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A296882, A296712, A296879, A296880.

Programs

Mathematica

z = 200; b = 9;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296879 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296880 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296881 *)