A296750 Numbers whose base-13 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 183, 195, 196, 208, 209, 210, 221, 222, 223, 224, 234, 235, 236, 237, 238, 247, 248, 249, 250, 251, 252

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 A296750-A296751 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-13 digits of 998 are 5,11,10; here #(rises) = 1 and #(falls) = 1, so 998 is in the sequence.

Mathematica

z = 200; b = 13; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296750 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296751 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296752 *)

Crossrefs

Cf. A296751, A296752, A296712.

Sequence in context: A044824 A048310 A043716 * A029958 A297280 A048324

Adjacent sequences: A296747 A296748 A296749 * A296751 A296752 A296753

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved