A296714 Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 110, 200, 210, 211, 220, 221, 300, 310, 311, 320, 321, 322, 330, 331, 332

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 A296712-A296714 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-10 digits of 332 are 3,3,2; here #(rises) = 0 and #(falls) = 1, so 332 is in the sequence.

Mathematica

z = 200; b = 10; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296712 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296713 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296714 *)

Crossrefs

Cf. A296712, A296713, A296712.

Sequence in context: A297270 A071590 A210589 * A297147 A325198 A098165

Adjacent sequences: A296711 A296712 A296713 * A296715 A296716 A296717

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved