A296876 Numbers whose base-8 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, 72, 73, 74

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 A296876-A296878 partition the natural numbers. See the guides at A296882 and A296712.

Examples

			The base-8 digits of 74 are 1,1,2; here #(pits) = 0 and #(peaks) = 0, so 74 is in the sequence.
		

Links

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

Crossrefs

Cf. A296882, A296712, A296877, A296878.

Programs

Mathematica

z = 200; b = 8;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296876 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296877 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296878 *)