A296867 Numbers whose base-5 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, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 37, 38, 39, 43, 44, 49, 50, 55, 56, 60, 61, 62, 63, 64, 68, 69, 74, 75, 80, 81, 85, 86, 87, 90, 91, 92, 93, 94, 99, 100, 105, 106, 110, 111, 112

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 A296867-A296869 partition the natural numbers. See the guides at A296882 and A296712.

Examples

			The base-5 digits of 112 are 4,2,2; here #(pits) = 0 and #(peaks) = 0, so 112 is in the sequence.
		

Links

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

Crossrefs

Cf. A296882, A296712, A296868, A296869.

Programs

Mathematica

z = 200; b = 5;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296867 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]    (* A296868 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]    (* A296869 *)