A296694 Numbers whose base-4 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments.

1, 2, 3, 5, 10, 15, 17, 18, 19, 21, 24, 25, 28, 29, 30, 33, 34, 35, 38, 39, 42, 44, 45, 46, 49, 50, 51, 54, 55, 59, 63, 65, 66, 67, 69, 74, 79, 81, 82, 83, 85, 88, 89, 92, 93, 94, 96, 101, 104, 105, 112, 117, 122, 124, 125, 126, 129, 130, 131, 133, 138, 143

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 A296694-A296696 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-4 digits of 143 are 2,0,3,3; here #(rises) = 1 and #(falls) = 1, so 143 is in the sequence.

Mathematica

z = 200; b = 4; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296694 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296695 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296696 *)

Crossrefs

Cf. A296695, A296696, A296700, A296712.

Sequence in context: A044815 A048301 A043707 * A297253 A014192 A250746

Adjacent sequences: A296691 A296692 A296693 * A296695 A296696 A296697

Keyword

nonn,base

Author

Clark Kimberling, Dec 21 2017

Status

approved