A296691 Numbers whose base-3 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments.

1, 2, 4, 8, 10, 11, 13, 15, 16, 19, 20, 23, 26, 28, 29, 31, 35, 37, 38, 40, 42, 43, 45, 49, 51, 52, 55, 56, 58, 62, 68, 71, 73, 74, 77, 80, 82, 83, 85, 89, 91, 92, 94, 96, 97, 100, 101, 104, 107, 109, 110, 112, 116, 118, 119, 121, 123, 124, 126, 130, 132

Offset

1,2

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 A296691-A296693 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-3 digits of 132 are 1,1,2,2,0; here #(rises) = #(falls) = 1, so 132 is in the sequence.

Mathematica

z = 200; b = 3; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296691 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296692 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296693 *)

Crossrefs

Cf. A296692, A296693, A296712.

Sequence in context: A256624 A247324 A043706 * A028836 A028838 A178332

Adjacent sequences: A296688 A296689 A296690 * A296692 A296693 A296694

Keyword

nonn,base

Author

Clark Kimberling, Dec 19 2017

Status

approved