A296764 - OEIS

%I #7 Jan 22 2023 20:45:17

%S 20,40,41,60,61,62,80,81,82,83,100,101,102,103,104,120,121,122,123,

%T 124,125,140,141,142,143,144,145,146,160,161,162,163,164,165,166,167,

%U 180,181,182,183,184,185,186,187,188,200,201,202,203,204,205,206,207,208

%N Numbers whose base-20 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 A296762-A296764 partition the natural numbers. See the guide at A296712.

%H Clark Kimberling, <a href="/A296764/b296764.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-20 digits of 208 are 10,8; here #(rises) = 0 and #(falls) = 2, so 208 is in the sequence.

%t z = 200; b = 20; d[n_] := Sign[Differences[IntegerDigits[n, b]]];

%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296762 *)

%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296763 *)

%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296764 *)

%Y Cf. A296762, A296763, A296712.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 08 2018