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%I #11 Jan 22 2023 20:50:54
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,20,21,22,23,26,27,31,32,36,37,
%T 40,41,42,43,47,48,52,53,56,57,58,60,61,62,63,64,65,66,67,68,72,73,76,
%U 77,78,80,84,85,86,87,90,91,95,97,98,99,102,103,104,105
%N Numbers whose base-4 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 A296864-A296866 partition the natural numbers. See the guides at A296882 and A296712.
%H Clark Kimberling, <a href="/A296864/b296864.txt">Table of n, a(n) for n = 1..10000</a>
%e The base-4 digits of 105 are 1, 2, 2, 1; here #(pits) = 0 and #(peaks) = 0, so 105 is in the sequence.
%t z = 200; b = 4;
%t d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296864 *)
%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296865 *)
%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296866 *)
%Y Cf. A296882, A296712, A296865, A296866.
%K nonn,base,easy
%O 1,2
%A _Clark Kimberling_, Jan 09 2018
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