A296902 Numbers whose base-16 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

288, 289, 304, 305, 306, 320, 321, 322, 323, 336, 337, 338, 339, 340, 352, 353, 354, 355, 356, 357, 368, 369, 370, 371, 372, 373, 374, 384, 385, 386, 387, 388, 389, 390, 391, 400, 401, 402, 403, 404, 405, 406, 407, 408, 416, 417, 418, 419, 420, 421, 422, 423

Offset: 1

Author

Clark Kimberling, Jan 12 2018

Keywords

• nonn
• base
• easy

Comments

A pit is an index i such that d(i-1) > d(i) < d(i+1); a peak is an index i such that d(i-1) < d(i) > d(i+1). The sequences A296900-A296902 partition the natural numbers. See the guides at A296712 and A296882.

Examples

			The base-16 digits of 74017 are 1,2,1,2,1; here #(pits) = 1 and #(peaks) = 2, so 74017 is in the sequence.
		

Links

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

Crossrefs

Cf. A296882, A296712, A296900, A296901.

Programs

Mathematica

z = 200; b = 16;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296900 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296901 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296902 *)