A296751 - OEIS

%I #7 Jan 27 2023 19:25:49

%S 15,16,17,18,19,20,21,22,23,24,25,29,30,31,32,33,34,35,36,37,38,43,44,

%T 45,46,47,48,49,50,51,57,58,59,60,61,62,63,64,71,72,73,74,75,76,77,85,

%U 86,87,88,89,90,99,100,101,102,103,113,114,115,116,127,128

%N Numbers whose base-13 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

%C 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 A296751-A296753 partition the natural numbers. See the guide at A296712.

%H Clark Kimberling, <a href="/A296751/b296751.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-13 digits of 1000 are 5,11,12; here #(rises) = 2 and #(falls) = 0, so 1000 is in the sequence.

%t z = 200; b = 13; d[n_] := Sign[Differences[IntegerDigits[n, b]]];

%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296750 *)

%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296751 *)

%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296752 *)

%Y Cf. A296750, A296752, A296712.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 08 2018