A296875 Numbers whose base-7 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

63, 64, 70, 71, 72, 77, 78, 79, 80, 84, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 119, 120, 121, 126, 127, 128, 129, 133, 134, 135, 136, 137, 140, 141, 142, 143, 144, 145, 175, 176, 177, 178, 182, 183, 184, 185, 186, 189, 190, 191, 192, 193, 194, 231, 232, 233

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 A296873-A296875 partition the natural numbers. See the guides at A296882 and A296712.

Examples

			The base-7 digits of 233 are 4,5,2; here #(pits) = 0 and #(peaks) = 1, so 233 is in the sequence.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..9999

Crossrefs

Cf. A296882, A296712, A296873, A296874.

Programs

Mathematica

z = 200; b = 7;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296873 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296874 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296875 *)