|
%I #7 Jan 27 2023 19:23:02
%S 7,14,15,21,22,23,28,29,30,31,35,36,37,38,39,42,43,44,45,46,47,49,56,
%T 98,105,106,112,113,147,154,155,161,162,163,168,169,170,196,203,204,
%U 210,211,212,217,218,219,220,224,225,226,227,245,252,253,259,260,261
%N Numbers whose base-7 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 A296703-A296705 partition the natural numbers. See the guide at A296712.
%H Clark Kimberling, <a href="/A296705/b296705.txt">Table of n, a(n) for n = 1..10000</a>
%e The base-7 digits of 261 are 5,2,2; here #(rises) = 0 and #(falls) = 2, so 261 is in the sequence.
%t z = 200; b = 7; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296703 *)
%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296704 *)
%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296705 *)
%Y Cf. A296703, A296704, A296712.
%K nonn,easy,base
%O 1,1
%A _Clark Kimberling_, Jan 08 2018
|
