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A296903 Numbers whose base-20 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

%I A296903 #12 Jan 21 2023 03:00:27
%S A296903 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 A296903 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U A296903 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67
%N A296903 Numbers whose base-20 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.
%C A296903 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 A296903-A296905 partition the natural numbers.
%C A296903 a(n) = n for n = 1..400, but not for n = 401. See the guides at A296712 and A296882.
%H A296903 Clark Kimberling, <a href="/A296903/b296903.txt">Table of n, a(n) for n = 1..10000</a>
%e A296903 The base-20 digits of 8822 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 8822 is in the sequence.
%t A296903 z = 200; b = 20;
%t A296903 d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
%t A296903 Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296903 *)
%t A296903 Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296904 *)
%t A296903 Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296905 *)
%Y A296903 Cf. A296882, A296712, A296904, A296905.
%K A296903 nonn,base,easy
%O A296903 1,2
%A A296903 _Clark Kimberling_, Jan 12 2018