A296711 Numbers whose base-9 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

9, 18, 19, 27, 28, 29, 36, 37, 38, 39, 45, 46, 47, 48, 49, 54, 55, 56, 57, 58, 59, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 81, 90, 162, 171, 172, 180, 181, 243, 252, 253, 261, 262, 263, 270, 271, 272, 324, 333, 334, 342, 343, 344, 351

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 A296709-A296711 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-9 digits of 351 are 4,3,0; here #(rises) = 0 and #(falls) = 2, so 351 is in the sequence.

Mathematica

z = 200; b = 9; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296709 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296710 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296711 *)

Crossrefs

Cf. A296709, A296710, A296712.

Sequence in context: A060993 A352380 A297267 * A297144 A107977 A257226

Adjacent sequences: A296708 A296709 A296710 * A296712 A296713 A296714

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved