A296876 - OEIS

%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 base-8 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 A296876-A296878 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 base-8 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