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

1,2

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A296882, A296712, A296862, A296863.

Sequence in context: A305462 A072618 A267762 * A069784 A259624 A178338

Adjacent sequences: A296858 A296859 A296860 * A296862 A296863 A296864

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 09 2018

Status

approved