A296903 Numbers whose base-20 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, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67

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 A296903-A296905 partition the natural numbers.

a(n) = n for n = 1..400, but not for n = 401. See the guides at A296712 and A296882.

Examples

			The base-20 digits of 8822 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 8822 is in the sequence.
		

Links

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

Crossrefs

Cf. A296882, A296712, A296904, A296905.

Programs

Mathematica

z = 200; b = 20;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296903 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296904 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296905 *)