A296697 Numbers whose base-5 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments.

1, 2, 3, 4, 6, 12, 18, 24, 26, 27, 28, 29, 31, 35, 36, 40, 41, 42, 45, 46, 47, 48, 51, 52, 53, 54, 57, 58, 59, 62, 65, 66, 67, 70, 71, 72, 73, 76, 77, 78, 79, 82, 83, 84, 88, 89, 93, 95, 96, 97, 98, 101, 102, 103, 104, 107, 108, 109, 113, 114, 119, 124, 126

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 A296697-A296699 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-5 digits of 126 are 1,0,0,1; here #(rises) = 1 and #(falls) = 1, so 126 is in the sequence.

Mathematica

z = 200; b = 5; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296697 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296698 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296699 *)
Select[Range[130], Total[Sign[Differences[IntegerDigits[#, 5]]]]==0&] (* Harvey P. Dale, Jul 30 2019 *)

Crossrefs

Cf. A296698, A296699, A296712.

Sequence in context: A044816 A048302 A043708 * A297256 A029952 A140494

Adjacent sequences: A296694 A296695 A296696 * A296698 A296699 A296700

Keyword

nonn,base

Author

Clark Kimberling, Dec 21 2017

Status

approved