A296759 Numbers whose base-16 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, 13, 14, 15, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 273, 288, 289, 304, 305, 306, 320, 321, 322, 323, 336, 337

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 A296759-A296761 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-16 digits of 2^20 + 1 are 1, 0, 0, 0, 0, 1; here #(rises) = 1 and #(falls) = 1, so 2^20 + 1 is in the sequence.

Mathematica

z = 200; b = 16; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296759 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296760 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296761 *)
Select[Range[400], Total[Sign[Differences[IntegerDigits[#, 16]]]]==0&] (* Harvey P. Dale, Aug 11 2021 *)

Crossrefs

Cf. A296760, A296761, A296712.

Sequence in context: A044827 A048313 A043719 * A029730 A297289 A048327

Adjacent sequences: A296756 A296757 A296758 * A296760 A296761 A296762

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved