A296757 Numbers whose base-15 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 81, 82, 83, 84, 85, 86, 87, 88, 89, 97, 98, 99, 100, 101, 102, 103, 104

Offset

1,1

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 A296756-A296758 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-15 digits of 2^20 + 6 are 1, 5, 10, 10, 5, 7; here #(rises) = 3 and #(falls) = 1, so 2^20 + 6 is in the sequence.

Mathematica

z = 200; b = 15; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296756 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296757 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296758 *)

Crossrefs

Cf. A296756, A296758, A296712.

Sequence in context: A145945 A165838 A217543 * A297287 A018822 A304488

Adjacent sequences: A296754 A296755 A296756 * A296758 A296759 A296760

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved