|
%I #7 Jan 27 2023 19:24:04
%S 9,18,19,27,28,29,36,37,38,39,45,46,47,48,49,54,55,56,57,58,59,63,64,
%T 65,66,67,68,69,72,73,74,75,76,77,78,79,81,90,162,171,172,180,181,243,
%U 252,253,261,262,263,270,271,272,324,333,334,342,343,344,351
%N Numbers whose base-9 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 A296709-A296711 partition the natural numbers. See the guide at A296712.
%H Clark Kimberling, <a href="/A296711/b296711.txt">Table of n, a(n) for n = 1..10000</a>
%e The base-9 digits of 351 are 4,3,0; here #(rises) = 0 and #(falls) = 2, so 351 is in the sequence.
%t z = 200; b = 9; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296709 *)
%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296710 *)
%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296711 *)
%Y Cf. A296709, A296710, A296712.
%K nonn,base,easy
%O 1,1
%A _Clark Kimberling_, Jan 08 2018
|
