A296702 - OEIS

%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