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

1,2

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A296704, A296705, A296712.

Sequence in context: A044818 A048304 A043710 * A297262 A029954 A048318

Adjacent sequences: A296700 A296701 A296702 * A296704 A296705 A296706

Keyword

nonn,easy,base

Author

Clark Kimberling, Jan 07 2018

Status

approved