%I #7 Jan 22 2023 20:51:06
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,30,
%T 31,32,33,34,37,38,39,43,44,49,50,55,56,60,61,62,63,64,68,69,74,75,80,
%U 81,85,86,87,90,91,92,93,94,99,100,105,106,110,111,112
%N Numbers whose base-5 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.
%C A pit is an index i such that d(i-1) > d(i) < d(i+1); a peak is an index i such that d(i-1) < d(i) > d(i+1). The sequences A296867-A296869 partition the natural numbers. See the guides at A296882 and A296712.
%H Clark Kimberling, <a href="/A296867/b296867.txt">Table of n, a(n) for n = 1..9999</a>
%e The base-5 digits of 112 are 4,2,2; here #(pits) = 0 and #(peaks) = 0, so 112 is in the sequence.
%t z = 200; b = 5;
%t d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296867 *)
%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296868 *)
%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296869 *)
%Y Cf. A296882, A296712, A296868, A296869.
%K nonn,base,easy
%O 1,2
%A _Clark Kimberling_, Jan 09 2018