A296864 Numbers whose base-4 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 26, 27, 31, 32, 36, 37, 40, 41, 42, 43, 47, 48, 52, 53, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 72, 73, 76, 77, 78, 80, 84, 85, 86, 87, 90, 91, 95, 97, 98, 99, 102, 103, 104, 105

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 105 are 1, 2, 2, 1; here #(pits) = 0 and #(peaks) = 0, so 105 is in the sequence.
		

Links

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

Crossrefs

Cf. A296882, A296712, A296865, A296866.

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 *)