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A296906 Numbers whose base-60 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

%I A296906 #16 Jan 21 2023 03:00:43
%S A296906 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 A296906 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U A296906 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67
%N A296906 Numbers whose base-60 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.
%C A296906 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 A296906..A296908 partition the natural numbers.
%C A296906 a(n) = n for n = 1..3600, but not for n = 3601. See the guides at A296712 and A296882.
%H A296906 Clark Kimberling, <a href="/A296906/b296906.txt">Table of n, a(n) for n = 1..10000</a>
%e A296906 The base-60 digits of 223262 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 223262 is in the sequence.
%t A296906 z = 200; b = 60;
%t A296906 d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
%t A296906 Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296906 *)
%t A296906 Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296907 *)
%t A296906 Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296908 *)
%Y A296906 Cf. A296882, A296712, A296907, A296908.
%K A296906 nonn,base,easy
%O A296906 1,2
%A A296906 _Clark Kimberling_, Jan 12 2018