A296900 Numbers whose base-16 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

1,2

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.

Links

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

Example

The base-16 digits of 4626 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 4626 is in the sequence.

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 *)

Crossrefs

Cf. A296882, A296712, A296901, A296902.

Sequence in context: A296891 A296894 A296897 * A296903 A296906 A104661

Adjacent sequences: A296897 A296898 A296899 * A296901 A296902 A296903

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 12 2018

Status

approved