A296703 Numbers whose base-7 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments.

1, 2, 3, 4, 5, 6, 8, 16, 24, 32, 40, 48, 50, 51, 52, 53, 54, 55, 57, 63, 64, 70, 71, 72, 77, 78, 79, 80, 84, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 104, 107, 108, 109, 110, 111, 114, 119, 120, 121, 126, 127, 128, 129, 133, 134, 135

Offset: 1

Author

Clark Kimberling, Jan 07 2018

Keywords

• nonn
• easy
• base

Comments

A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296703-A296705 partition the natural numbers. See the guide at A296712.

Examples

			The base-7 digits of 135 are 2,5,2; here #(rises) = 1 and #(falls) = 1, so 135 is in the sequence.
		

Links

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

Crossrefs

Cf. A296704, A296705, A296712.

Programs

Mathematica

z = 200; b = 7; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296703 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296704 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296705 *)