A296897 Numbers whose base-15 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 A296897-A296899 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-15 digits of 3842 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 3842 is in the sequence.

Mathematica

z = 200; b = 15;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296897 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296898 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296899 *)

Crossrefs

Cf. A296882, A296712, A296898, A296899.

Sequence in context: A296888 A296891 A296894 * A296900 A296903 A296906

Adjacent sequences: A296894 A296895 A296896 * A296898 A296899 A296900

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 12 2018

Status

approved