A296700 - OEIS

%I #8 Jan 27 2023 19:09:59

%S 1,2,3,4,5,7,14,21,28,35,37,38,39,40,41,43,48,49,54,55,56,60,61,62,63,

%T 66,67,68,69,70,73,74,75,76,77,80,81,82,83,86,90,91,92,96,97,98,99,

%U 102,103,104,105,106,109,110,111,112,113,116,117,118,119,123

%N Numbers whose base-6 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 A296700-A296702 partition the natural numbers. See the guide at A296712.

%H Clark Kimberling, <a href="/A296700/b296700.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-6 digits of 123 are 3,2,3; here #(rises) = 1 and #(falls) = 1, so 123 is in the sequence.

%t z = 200; b = 6; d[n_] := Sign[Differences[IntegerDigits[n, b]]];

%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296700 *)

%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296701 *)

%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296702 *)

%Y Cf. A296701, A296702, A296712.

%K nonn,base

%O 1,2

%A _Clark Kimberling_, Dec 21 2017