|
%I #7 Jan 22 2023 20:50:58
%S 17,18,19,33,34,35,38,39,49,50,51,54,55,59,69,70,71,74,75,79,81,82,83,
%T 133,134,135,138,139,143,145,146,147,154,155,159,161,162,163,166,167,
%U 197,198,199,202,203,207,209,210,211,218,219,223,225,226,227,230
%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="/A296865/b296865.txt">Table of n, a(n) for n = 1..9999</a>
%e The base-4 digits of 230 are 3, 2, 1, 2; here #(pits) = 1 and #(peaks) = 0, so 230 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, A296864, A296866.
%K nonn,base,easy
%O 1,1
%A _Clark Kimberling_, Jan 09 2018
|
