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

Author

Clark Kimberling, Jan 08 2018

Keywords

• nonn
• base
• easy

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A296760, A296761, A296712.

Programs

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 *)