A296861 Numbers whose base-3 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 17, 18, 21, 22, 24, 25, 26, 27, 28, 29, 30, 33, 34, 36, 39, 40, 41, 44, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 63, 66, 67, 68, 69, 70, 72, 75, 76, 78, 79, 80, 81, 82, 83, 85, 86, 89, 90, 96, 97, 99, 102, 103

Offset: 1

Author

Clark Kimberling, Jan 09 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 A296861-A296863 partition the natural numbers. See the guides at A296882 and A296712.

Examples

			The base-3 digits of 103 are 1, 0, 2, 1, 1; here #(pits) = 1 and #(peaks) = 1, so 103 is in the sequence.
		

Links

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

Crossrefs

Cf. A296882, A296712, A296862, A296863.

Programs

Mathematica

z = 200; b = 3;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296861 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296862 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296863 *)