A296760 Numbers whose base-16 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 103, 104, 105, 106

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 A296759-A296761 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-16 digits of 106 are 6,10; here #(rises) = 1 and #(falls) = 0, so 106 is in the sequence.

Mathematica

z = 200; b = 16; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296759 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296760 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296761 *)
rgf16Q[n_]:=Total[Sign[#]&/@Differences[IntegerDigits[n, 16]]]>0; Select[Range[150], rgf16Q] (* Harvey P. Dale, Nov 26 2023 *)

Crossrefs

Cf. A296759, A296761, A296712.

Sequence in context: A004459 A347282 A004507 * A297290 A270044 A018823

Adjacent sequences: A296757 A296758 A296759 * A296761 A296762 A296763

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved