A296700 Numbers whose base-6 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments.

1, 2, 3, 4, 5, 7, 14, 21, 28, 35, 37, 38, 39, 40, 41, 43, 48, 49, 54, 55, 56, 60, 61, 62, 63, 66, 67, 68, 69, 70, 73, 74, 75, 76, 77, 80, 81, 82, 83, 86, 90, 91, 92, 96, 97, 98, 99, 102, 103, 104, 105, 106, 109, 110, 111, 112, 113, 116, 117, 118, 119, 123

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 A296700-A296702 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-6 digits of 123 are 3,2,3; here #(rises) = 1 and #(falls) = 1, so 123 is in the sequence.

Mathematica

z = 200; b = 6; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296700 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296701 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296702 *)

Crossrefs

Cf. A296701, A296702, A296712.

Sequence in context: A044817 A048303 A043709 * A297259 A029953 A048317

Adjacent sequences: A296697 A296698 A296699 * A296701 A296702 A296703

Keyword

nonn,base

Author

Clark Kimberling, Dec 21 2017

Status

approved