|
%I #9 Jan 27 2023 19:09:18
%S 6,12,13,18,19,20,24,25,26,27,30,31,32,33,34,36,42,72,78,79,84,85,108,
%T 114,115,120,121,122,126,127,128,144,150,151,156,157,158,162,163,164,
%U 165,168,169,170,171,180,186,187,192,193,194,198,199,200,201,204
%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="/A296702/b296702.txt">Table of n, a(n) for n = 1..10000</a>
%e The base-6 digits of 224 are 5,4,0; here #(rises) = 0 and #(falls) = 2, so 204 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. A296700, A296701, A296712.
%K nonn,easy,base
%O 1,1
%A _Clark Kimberling_, Jan 07 2018
|
