A296883 Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.

101, 102, 103, 104, 105, 106, 107, 108, 109, 201, 202, 203, 204, 205, 206, 207, 208, 209, 212, 213, 214, 215, 216, 217, 218, 219, 301, 302, 303, 304, 305, 306, 307, 308, 309, 312, 313, 314, 315, 316, 317, 318, 319, 323, 324, 325, 326, 327, 328, 329, 401, 402

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 A296882-A296883 partition the natural numbers. See the guides at A296712 and A296882.

Examples

			The base-10 digits of 21212 are 2,1,2,1,2; here #(pits) = 2 and #(peaks) = 1, so 21212 is in the sequence.
		

Links

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

Crossrefs

Cf. A296882, A296712, A296882, A296884.

Programs

Mathematica

z = 200; b = 10;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296882 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296883 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296884 *)