%I #7 Jan 21 2023 18:02:36
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,72,73,74
%N Numbers whose base8 digits d(m), d(m1), ..., d(0) have #(pits) = #(peaks); see Comments.
%C A pit is an index i such that d(i1) > d(i) < d(i+1); a peak is an index i such that d(i1) < d(i) > d(i+1). The sequences A296876A296878 partition the natural numbers. See the guides at A296882 and A296712.
%H Clark Kimberling, <a href="/A296876/b296876.txt">Table of n, a(n) for n = 1..10000</a>
%e The base8 digits of 74 are 1,1,2; here #(pits) = 0 and #(peaks) = 0, so 74 is in the sequence.
%t z = 200; b = 8;
%t d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
%t Select[Range [z], Count[d[#], 2] == Count[d[#], 2] &] (* A296876 *)
%t Select[Range [z], Count[d[#], 2] < Count[d[#], 2] &] (* A296877 *)
%t Select[Range [z], Count[d[#], 2] > Count[d[#], 2] &] (* A296878 *)
%Y Cf. A296882, A296712, A296877, A296878.
%K nonn,base,easy
%O 1,2
%A _Clark Kimberling_, Jan 09 2018
