A296762 - OEIS

A296762

Numbers whose base-20 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

%I #7 Jan 22 2023 18:18:48

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,42,63,84,105,126,

%T 147,168,189,210,231,252,273,294,315,336,357,378,399,401,402,403,404,

%U 405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,421

%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="/A296762/b296762.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-20 digits of 421 are 1,1,1; here #(rises) = 0 and #(falls) = 0, so 421 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. A296763, A296764, A296712.

%K nonn,base,easy

%O 1,2

%A _Clark Kimberling_, Jan 08 2018