A296866 Numbers whose base-4 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

24, 25, 28, 29, 30, 44, 45, 46, 88, 89, 92, 93, 94, 96, 100, 101, 108, 109, 110, 112, 116, 117, 120, 121, 122, 172, 173, 174, 176, 180, 181, 184, 185, 186, 260, 264, 265, 268, 269, 270, 344, 345, 348, 349, 350, 352, 356, 357, 364, 365, 366, 368, 372, 373

Offset: 1

Author

Clark Kimberling, Jan 09 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 A296864-A296866 partition the natural numbers. See the guides at A296882 and A296712.

Examples

			The base-4 digits of 373 are 1,1,3,1,1; here #(pits) = 0 and #(peaks) = 2, so 373 is in the sequence.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..9999

Crossrefs

Cf. A296882, A296712, A296864, A296865.

Programs

Mathematica

z = 200; b = 4;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296864 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296865 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296866 *)