A296906 Numbers whose base-60 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 A296906..A296908 partition the natural numbers.

a(n) = n for n = 1..3600, but not for n = 3601. See the guides at A296712 and A296882.

Links

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

Example

The base-60 digits of 223262 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 223262 is in the sequence.

Mathematica

z = 200; b = 60;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296906 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296907 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296908 *)

Crossrefs

Cf. A296882, A296712, A296907, A296908.

Sequence in context: A296897 A296900 A296903 * A104661 A069782 A088480

Adjacent sequences: A296903 A296904 A296905 * A296907 A296908 A296909

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 12 2018

Status

approved