A296696 Numbers whose base-4 digits d(m), d(m-1), ... d(0) have #(rises) < #(falls); see Comments.

4, 8, 9, 12, 13, 14, 16, 20, 32, 36, 37, 40, 41, 48, 52, 53, 56, 57, 58, 60, 61, 62, 64, 68, 72, 73, 76, 77, 78, 80, 84, 100, 116, 120, 121, 128, 132, 136, 137, 140, 141, 142, 144, 145, 146, 147, 148, 149, 152, 153, 156, 157, 158, 160, 164, 165, 168, 169

Offset

1,1

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 196 are 3,0,1,0; here #(rises) = 1 and #(falls) = 2, so 196 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. A296694, A296695, A296712.

Sequence in context: A306976 A266142 A297252 * A297129 A078137 A294574

Adjacent sequences: A296693 A296694 A296695 * A296697 A296698 A296699

Keyword

nonn,base

Author

Clark Kimberling, Dec 21 2017

Extensions

Example corrected by Harvey P. Dale, Sep 04 2018

Status

approved